jc.tex (41202B)
1 %Clause Contingente 01 - jc 2 \begin{frame} 3 \begin{figure}[h!] 4 \centering 5 \begin{tikzpicture}[ 6 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 7 lettre/.style={ 8 on chain, 9 draw, 10 circle, 11 minimum size=1cm 12 }, 13 chiffre/.style={ 14 node distance = 0.75cm 15 }, 16 arr/.style={ 17 ->, 18 >=triangle 90 19 } 20 ] 21 \node[lettre] (1) {$\lnot x1$} ; 22 \node[lettre] (5) {$x2$} ; 23 \node[lettre] (3) {$\lnot x2$} ; 24 \node[lettre] (6) {$x3$} ; 25 \node[lettre] (4) {$\lnot x3$} ; 26 \node[lettre] (7) {$x4$} ; 27 \node[lettre] (2) {$\lnot x4$} ; 28 \node[lettre] (8) {$x1$} ; 29 30 \end{tikzpicture} 31 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 32 \label{fig:clause-conting} 33 \end{figure} 34 \end{frame} 35 36 %Clause Contingente 02 - jc 37 \begin{frame} 38 \begin{figure}[h!] 39 \centering 40 \begin{tikzpicture}[ 41 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 42 lettre/.style={ 43 on chain, 44 draw, 45 circle, 46 minimum size=1cm 47 }, 48 chiffre/.style={ 49 node distance = 0.75cm 50 }, 51 arr/.style={ 52 ->, 53 >=triangle 90 54 } 55 ] 56 \node[lettre] (1) {$\lnot x1$} ; 57 \node[lettre] (5) {$x2$} ; 58 \node[lettre] (3) {$\lnot x2$} ; 59 \node[lettre] (6) {$x3$} ; 60 \node[lettre] (4) {$\lnot x3$} ; 61 \node[lettre] (7) {$x4$} ; 62 \node[lettre] (2) {$\lnot x4$} ; 63 \node[lettre] (8) {$x1$} ; 64 65 66 \draw[arr] (1) -- (5) ; 67 68 \end{tikzpicture} 69 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 70 \label{fig:clause-conting} 71 \end{figure} 72 \end{frame} 73 74 %Clause Contingente 03 - jc 75 \begin{frame} 76 \begin{figure}[h!] 77 \centering 78 \begin{tikzpicture}[ 79 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 80 lettre/.style={ 81 on chain, 82 draw, 83 circle, 84 minimum size=1cm 85 }, 86 chiffre/.style={ 87 node distance = 0.75cm 88 }, 89 arr/.style={ 90 ->, 91 >=triangle 90 92 } 93 ] 94 \node[lettre] (1) {$\lnot x1$} ; 95 \node[lettre] (5) {$x2$} ; 96 \node[lettre] (3) {$\lnot x2$} ; 97 \node[lettre] (6) {$x3$} ; 98 \node[lettre] (4) {$\lnot x3$} ; 99 \node[lettre] (7) {$x4$} ; 100 \node[lettre] (2) {$\lnot x4$} ; 101 \node[lettre] (8) {$x1$} ; 102 103 104 \draw[arr] (1) -- (5) ; 105 \draw[arr] (3) -- (8) ; 106 \end{tikzpicture} 107 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 108 \label{fig:clause-conting} 109 \end{figure} 110 \end{frame} 111 112 %Clause Contingente 04 - jc 113 \begin{frame} 114 \begin{figure}[h!] 115 \centering 116 \begin{tikzpicture}[ 117 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 118 lettre/.style={ 119 on chain, 120 draw, 121 circle, 122 minimum size=1cm 123 }, 124 chiffre/.style={ 125 node distance = 0.75cm 126 }, 127 arr/.style={ 128 ->, 129 >=triangle 90 130 } 131 ] 132 \node[lettre] (1) {$\lnot x1$} ; 133 \node[lettre] (5) {$x2$} ; 134 \node[lettre] (3) {$\lnot x2$} ; 135 \node[lettre] (6) {$x3$} ; 136 \node[lettre] (4) {$\lnot x3$} ; 137 \node[lettre] (7) {$x4$} ; 138 \node[lettre] (2) {$\lnot x4$} ; 139 \node[lettre] (8) {$x1$} ; 140 141 \draw[arr] (1) -- (5) ; 142 \draw[arr] (3) -- (8) ; 143 \draw[arr] (4) -- (7) ; 144 \end{tikzpicture} 145 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 146 \label{fig:clause-conting} 147 \end{figure} 148 \end{frame} 149 150 %Clause Contingente 05 - jc 151 \begin{frame} 152 \begin{figure}[h!] 153 \centering 154 \begin{tikzpicture}[ 155 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 156 lettre/.style={ 157 on chain, 158 draw, 159 circle, 160 minimum size=1cm 161 }, 162 chiffre/.style={ 163 node distance = 0.75cm 164 }, 165 arr/.style={ 166 ->, 167 >=triangle 90 168 } 169 ] 170 \node[lettre] (1) {$\lnot x1$} ; 171 \node[lettre] (5) {$x2$} ; 172 \node[lettre] (3) {$\lnot x2$} ; 173 \node[lettre] (6) {$x3$} ; 174 \node[lettre] (4) {$\lnot x3$} ; 175 \node[lettre] (7) {$x4$} ; 176 \node[lettre] (2) {$\lnot x4$} ; 177 \node[lettre] (8) {$x1$} ; 178 179 \draw[arr] (1) -- (5) ; 180 \draw[arr] (3) -- (8) ; 181 \draw[arr] (2) -- (6) ; 182 \draw[arr] (4) -- (7) ; 183 \end{tikzpicture} 184 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 185 \label{fig:clause-conting} 186 \end{figure} 187 \end{frame} 188 189 %Clause Contingente 06 - jc 190 \begin{frame} 191 \begin{figure}[h!] 192 \centering 193 \begin{tikzpicture}[ 194 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 195 lettre/.style={ 196 on chain, 197 draw, 198 circle, 199 minimum size=1cm 200 }, 201 chiffre/.style={ 202 node distance = 0.75cm 203 }, 204 arr/.style={ 205 ->, 206 >=triangle 90 207 } 208 ] 209 \node[lettre] (1) {$\lnot x1$} ; 210 \node[lettre] (5) {$x2$} ; 211 \node[lettre] (3) {$\lnot x2$} ; 212 \node[lettre] (6) {$x3$} ; 213 \node[lettre] (4) {$\lnot x3$} ; 214 \node[lettre] (7) {$x4$} ; 215 \node[lettre] (2) {$\lnot x4$} ; 216 \node[lettre] (8) {$x1$} ; 217 218 \node[chiffre, above right of=1] {1} ; 219 220 \draw[arr] (1) -- (5) ; 221 \draw[arr] (3) -- (8) ; 222 \draw[arr] (2) -- (6) ; 223 \draw[arr] (4) -- (7) ; 224 \end{tikzpicture} 225 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 226 \label{fig:clause-conting} 227 \end{figure} 228 \end{frame} 229 230 %Clause Contingente 07 - jc 231 \begin{frame} 232 \begin{figure}[h!] 233 \centering 234 \begin{tikzpicture}[ 235 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 236 lettre/.style={ 237 on chain, 238 draw, 239 circle, 240 minimum size=1cm 241 }, 242 chiffre/.style={ 243 node distance = 0.75cm 244 }, 245 arr/.style={ 246 ->, 247 >=triangle 90 248 } 249 ] 250 \node[lettre] (1) {$\lnot x1$} ; 251 \node[lettre] (5) {$x2$} ; 252 \node[lettre] (3) {$\lnot x2$} ; 253 \node[lettre] (6) {$x3$} ; 254 \node[lettre] (4) {$\lnot x3$} ; 255 \node[lettre] (7) {$x4$} ; 256 \node[lettre] (2) {$\lnot x4$} ; 257 \node[lettre] (8) {$x1$} ; 258 259 \node[chiffre, above right of=1] {1} ; 260 \node[chiffre, above left of=2] {2} ; 261 262 \draw[arr] (1) -- (5) ; 263 \draw[arr] (3) -- (8) ; 264 \draw[arr] (2) -- (6) ; 265 \draw[arr] (4) -- (7) ; 266 \end{tikzpicture} 267 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 268 \label{fig:clause-conting} 269 \end{figure} 270 \end{frame} 271 272 %Clause Contingente 08 - jc 273 \begin{frame} 274 \begin{figure}[h!] 275 \centering 276 \begin{tikzpicture}[ 277 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 278 lettre/.style={ 279 on chain, 280 draw, 281 circle, 282 minimum size=1cm 283 }, 284 chiffre/.style={ 285 node distance = 0.75cm 286 }, 287 arr/.style={ 288 ->, 289 >=triangle 90 290 } 291 ] 292 \node[lettre] (1) {$\lnot x1$} ; 293 \node[lettre] (5) {$x2$} ; 294 \node[lettre] (3) {$\lnot x2$} ; 295 \node[lettre] (6) {$x3$} ; 296 \node[lettre] (4) {$\lnot x3$} ; 297 \node[lettre] (7) {$x4$} ; 298 \node[lettre] (2) {$\lnot x4$} ; 299 \node[lettre] (8) {$x1$} ; 300 301 \node[chiffre, above right of=1] {1} ; 302 \node[chiffre, below right of=3] {3} ; 303 \node[chiffre, above left of=2] {2} ; 304 305 \draw[arr] (1) -- (5) ; 306 \draw[arr] (3) -- (8) ; 307 \draw[arr] (2) -- (6) ; 308 \draw[arr] (4) -- (7) ; 309 \end{tikzpicture} 310 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 311 \label{fig:clause-conting} 312 \end{figure} 313 \end{frame} 314 315 %Clause Contingente 09 - jc 316 \begin{frame} 317 \begin{figure}[h!] 318 \centering 319 \begin{tikzpicture}[ 320 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 321 lettre/.style={ 322 on chain, 323 draw, 324 circle, 325 minimum size=1cm 326 }, 327 chiffre/.style={ 328 node distance = 0.75cm 329 }, 330 arr/.style={ 331 ->, 332 >=triangle 90 333 } 334 ] 335 \node[lettre] (1) {$\lnot x1$} ; 336 \node[lettre] (5) {$x2$} ; 337 \node[lettre] (3) {$\lnot x2$} ; 338 \node[lettre] (6) {$x3$} ; 339 \node[lettre] (4) {$\lnot x3$} ; 340 \node[lettre] (7) {$x4$} ; 341 \node[lettre] (2) {$\lnot x4$} ; 342 \node[lettre] (8) {$x1$} ; 343 344 \node[chiffre, above right of=1] {1} ; 345 \node[chiffre, below right of=3] {3} ; 346 \node[chiffre, below left of=4] {4} ; 347 \node[chiffre, above left of=2] {2} ; 348 349 \draw[arr] (1) -- (5) ; 350 \draw[arr] (3) -- (8) ; 351 \draw[arr] (2) -- (6) ; 352 \draw[arr] (4) -- (7) ; 353 \end{tikzpicture} 354 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 355 \label{fig:clause-conting} 356 \end{figure} 357 \end{frame} 358 359 %Clause Contingente 10 - jc 360 \begin{frame} 361 \begin{figure}[h!] 362 \centering 363 \begin{tikzpicture}[ 364 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 365 lettre/.style={ 366 on chain, 367 draw, 368 circle, 369 minimum size=1cm 370 }, 371 chiffre/.style={ 372 node distance = 0.75cm 373 }, 374 arr/.style={ 375 ->, 376 >=triangle 90 377 } 378 ] 379 \node[lettre] (1) {$\lnot x1$} ; 380 \node[lettre] (5) {$x2$} ; 381 \node[lettre] (3) {$\lnot x2$} ; 382 \node[lettre] (6) {$x3$} ; 383 \node[lettre] (4) {$\lnot x3$} ; 384 \node[lettre] (7) {$x4$} ; 385 \node[lettre] (2) {$\lnot x4$} ; 386 \node[lettre] (8) {$x1$} ; 387 388 \node[chiffre, above right of=1] {1} ; 389 \node[chiffre, above right of=5] {5} ; 390 \node[chiffre, below right of=3] {3} ; 391 \node[chiffre, below left of=4] {4} ; 392 \node[chiffre, above left of=2] {2} ; 393 394 \draw[arr] (1) -- (5) ; 395 \draw[arr] (3) -- (8) ; 396 \draw[arr] (2) -- (6) ; 397 \draw[arr] (4) -- (7) ; 398 \end{tikzpicture} 399 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 400 \label{fig:clause-conting} 401 \end{figure} 402 \end{frame} 403 404 %Clause Contingente 11 - jc 405 \begin{frame} 406 \begin{figure}[h!] 407 \centering 408 \begin{tikzpicture}[ 409 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 410 lettre/.style={ 411 on chain, 412 draw, 413 circle, 414 minimum size=1cm 415 }, 416 chiffre/.style={ 417 node distance = 0.75cm 418 }, 419 arr/.style={ 420 ->, 421 >=triangle 90 422 } 423 ] 424 \node[lettre] (1) {$\lnot x1$} ; 425 \node[lettre] (5) {$x2$} ; 426 \node[lettre] (3) {$\lnot x2$} ; 427 \node[lettre] (6) {$x3$} ; 428 \node[lettre] (4) {$\lnot x3$} ; 429 \node[lettre] (7) {$x4$} ; 430 \node[lettre] (2) {$\lnot x4$} ; 431 \node[lettre] (8) {$x1$} ; 432 433 \node[chiffre, above right of=1] {1} ; 434 \node[chiffre, above right of=5] {5} ; 435 \node[chiffre, below right of=3] {3} ; 436 \node[chiffre, below right of=6] {6} ; 437 \node[chiffre, below left of=4] {4} ; 438 \node[chiffre, above left of=2] {2} ; 439 440 \draw[arr] (1) -- (5) ; 441 \draw[arr] (3) -- (8) ; 442 \draw[arr] (2) -- (6) ; 443 \draw[arr] (4) -- (7) ; 444 \end{tikzpicture} 445 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 446 \label{fig:clause-conting} 447 \end{figure} 448 \end{frame} 449 450 %Clause Contingente 12 - jc 451 \begin{frame} 452 \begin{figure}[h!] 453 \centering 454 \begin{tikzpicture}[ 455 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 456 lettre/.style={ 457 on chain, 458 draw, 459 circle, 460 minimum size=1cm 461 }, 462 chiffre/.style={ 463 node distance = 0.75cm 464 }, 465 arr/.style={ 466 ->, 467 >=triangle 90 468 } 469 ] 470 \node[lettre] (1) {$\lnot x1$} ; 471 \node[lettre] (5) {$x2$} ; 472 \node[lettre] (3) {$\lnot x2$} ; 473 \node[lettre] (6) {$x3$} ; 474 \node[lettre] (4) {$\lnot x3$} ; 475 \node[lettre] (7) {$x4$} ; 476 \node[lettre] (2) {$\lnot x4$} ; 477 \node[lettre] (8) {$x1$} ; 478 479 \node[chiffre, above right of=1] {1} ; 480 \node[chiffre, above right of=5] {5} ; 481 \node[chiffre, below right of=3] {3} ; 482 \node[chiffre, below right of=6] {6} ; 483 \node[chiffre, below left of=4] {4} ; 484 \node[chiffre, below left of=7] {7} ; 485 \node[chiffre, above left of=2] {2} ; 486 487 \draw[arr] (1) -- (5) ; 488 \draw[arr] (3) -- (8) ; 489 \draw[arr] (2) -- (6) ; 490 \draw[arr] (4) -- (7) ; 491 \end{tikzpicture} 492 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 493 \label{fig:clause-conting} 494 \end{figure} 495 \end{frame} 496 497 %Clause Contingente 13 - jc 498 \begin{frame} 499 \begin{figure}[h!] 500 \centering 501 \begin{tikzpicture}[ 502 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 503 lettre/.style={ 504 on chain, 505 draw, 506 circle, 507 minimum size=1cm 508 }, 509 chiffre/.style={ 510 node distance = 0.75cm 511 }, 512 arr/.style={ 513 ->, 514 >=triangle 90 515 } 516 ] 517 \node[lettre] (1) {$\lnot x1$} ; 518 \node[lettre] (5) {$x2$} ; 519 \node[lettre] (3) {$\lnot x2$} ; 520 \node[lettre] (6) {$x3$} ; 521 \node[lettre] (4) {$\lnot x3$} ; 522 \node[lettre] (7) {$x4$} ; 523 \node[lettre] (2) {$\lnot x4$} ; 524 \node[lettre] (8) {$x1$} ; 525 526 \node[chiffre, above right of=1] {1} ; 527 \node[chiffre, above right of=5] {5} ; 528 \node[chiffre, below right of=3] {3} ; 529 \node[chiffre, below right of=6] {6} ; 530 \node[chiffre, below left of=4] {4} ; 531 \node[chiffre, below left of=7] {7} ; 532 \node[chiffre, above left of=2] {2} ; 533 \node[chiffre, above left of=8] {8} ; 534 535 \draw[arr] (1) -- (5) ; 536 \draw[arr] (3) -- (8) ; 537 \draw[arr] (2) -- (6) ; 538 \draw[arr] (4) -- (7) ; 539 \end{tikzpicture} 540 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 541 \label{fig:clause-conting} 542 \end{figure} 543 \end{frame} 544 545 %Clause Contingente 14 - jc 546 \begin{frame} 547 \begin{figure}[h!] 548 \centering 549 \begin{tikzpicture}[ 550 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 551 lettre/.style={ 552 on chain, 553 draw, 554 circle, 555 minimum size=1cm 556 }, 557 chiffre/.style={ 558 node distance = 0.75cm 559 }, 560 arr/.style={ 561 ->, 562 >=triangle 90 563 } 564 ] 565 \node[lettre] (1) {$\lnot x1$} ; 566 \node[lettre] (5) {$x2$} ; 567 \node[lettre] (3) {$\lnot x2$} ; 568 \node[lettre] (6) {$x3$} ; 569 \node[lettre] (4) {$\lnot x3$} ; 570 \node[lettre] (7) {$x4$} ; 571 \node[lettre] (2) {$\lnot x4$} ; 572 \node[lettre] (8) {$x1$} ; 573 574 \node[left of=8] {\textcolor{green!75!black}{vrai}} ; 575 576 \node[chiffre, above right of=1] {1} ; 577 \node[chiffre, above right of=5] {5} ; 578 \node[chiffre, below right of=3] {3} ; 579 \node[chiffre, below right of=6] {6} ; 580 \node[chiffre, below left of=4] {4} ; 581 \node[chiffre, below left of=7] {7} ; 582 \node[chiffre, above left of=2] {2} ; 583 \node[chiffre, above left of=8] {8} ; 584 585 \draw[arr] (1) -- (5) ; 586 \draw[arr] (3) -- (8) ; 587 \draw[arr] (2) -- (6) ; 588 \draw[arr] (4) -- (7) ; 589 \end{tikzpicture} 590 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 591 \label{fig:clause-conting} 592 \end{figure} 593 \end{frame} 594 595 %Clause Contingente 15 - jc 596 \begin{frame} 597 \begin{figure}[h!] 598 \centering 599 \begin{tikzpicture}[ 600 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 601 lettre/.style={ 602 on chain, 603 draw, 604 circle, 605 minimum size=1cm 606 }, 607 chiffre/.style={ 608 node distance = 0.75cm 609 }, 610 arr/.style={ 611 ->, 612 >=triangle 90 613 } 614 ] 615 \node[lettre] (1) {$\lnot x1$} ; 616 \node[lettre] (5) {$x2$} ; 617 \node[lettre] (3) {$\lnot x2$} ; 618 \node[lettre] (6) {$x3$} ; 619 \node[lettre] (4) {$\lnot x3$} ; 620 \node[lettre] (7) {$x4$} ; 621 \node[lettre] (2) {$\lnot x4$} ; 622 \node[lettre] (8) {$x1$} ; 623 624 \node[right of=1] {\textcolor{red}{faux}} ; 625 \node[left of=8] {\textcolor{green!75!black}{vrai}} ; 626 627 \node[chiffre, above right of=1] {1} ; 628 \node[chiffre, above right of=5] {5} ; 629 \node[chiffre, below right of=3] {3} ; 630 \node[chiffre, below right of=6] {6} ; 631 \node[chiffre, below left of=4] {4} ; 632 \node[chiffre, below left of=7] {7} ; 633 \node[chiffre, above left of=2] {2} ; 634 \node[chiffre, above left of=8] {8} ; 635 636 \draw[arr] (1) -- (5) ; 637 \draw[arr] (3) -- (8) ; 638 \draw[arr] (2) -- (6) ; 639 \draw[arr] (4) -- (7) ; 640 \end{tikzpicture} 641 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 642 \label{fig:clause-conting} 643 \end{figure} 644 \end{frame} 645 646 %Clause Contingente 16 - jc 647 \begin{frame} 648 \begin{figure}[h!] 649 \centering 650 \begin{tikzpicture}[ 651 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 652 lettre/.style={ 653 on chain, 654 draw, 655 circle, 656 minimum size=1cm 657 }, 658 chiffre/.style={ 659 node distance = 0.75cm 660 }, 661 arr/.style={ 662 ->, 663 >=triangle 90 664 } 665 ] 666 \node[lettre] (1) {$\lnot x1$} ; 667 \node[lettre] (5) {$x2$} ; 668 \node[lettre] (3) {$\lnot x2$} ; 669 \node[lettre] (6) {$x3$} ; 670 \node[lettre] (4) {$\lnot x3$} ; 671 \node[lettre] (7) {$x4$} ; 672 \node[lettre] (2) {$\lnot x4$} ; 673 \node[lettre] (8) {$x1$} ; 674 675 \node[right of=1] {\textcolor{red}{faux}} ; 676 \node[left of=7] {\textcolor{green!75!black}{vrai}} ; 677 \node[left of=8] {\textcolor{green!75!black}{vrai}} ; 678 679 \node[chiffre, above right of=1] {1} ; 680 \node[chiffre, above right of=5] {5} ; 681 \node[chiffre, below right of=3] {3} ; 682 \node[chiffre, below right of=6] {6} ; 683 \node[chiffre, below left of=4] {4} ; 684 \node[chiffre, below left of=7] {7} ; 685 \node[chiffre, above left of=2] {2} ; 686 \node[chiffre, above left of=8] {8} ; 687 688 \draw[arr] (1) -- (5) ; 689 \draw[arr] (3) -- (8) ; 690 \draw[arr] (2) -- (6) ; 691 \draw[arr] (4) -- (7) ; 692 \end{tikzpicture} 693 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 694 \label{fig:clause-conting} 695 \end{figure} 696 \end{frame} 697 698 %Clause Contingente 17 - jc 699 \begin{frame} 700 \begin{figure}[h!] 701 \centering 702 \begin{tikzpicture}[ 703 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 704 lettre/.style={ 705 on chain, 706 draw, 707 circle, 708 minimum size=1cm 709 }, 710 chiffre/.style={ 711 node distance = 0.75cm 712 }, 713 arr/.style={ 714 ->, 715 >=triangle 90 716 } 717 ] 718 \node[lettre] (1) {$\lnot x1$} ; 719 \node[lettre] (5) {$x2$} ; 720 \node[lettre] (3) {$\lnot x2$} ; 721 \node[lettre] (6) {$x3$} ; 722 \node[lettre] (4) {$\lnot x3$} ; 723 \node[lettre] (7) {$x4$} ; 724 \node[lettre] (2) {$\lnot x4$} ; 725 \node[lettre] (8) {$x1$} ; 726 727 \node[right of=1] {\textcolor{red}{faux}} ; 728 \node[left of=7] {\textcolor{green!75!black}{vrai}} ; 729 \node[left of=2] {\textcolor{red}{faux}} ; 730 \node[left of=8] {\textcolor{green!75!black}{vrai}} ; 731 732 \node[chiffre, above right of=1] {1} ; 733 \node[chiffre, above right of=5] {5} ; 734 \node[chiffre, below right of=3] {3} ; 735 \node[chiffre, below right of=6] {6} ; 736 \node[chiffre, below left of=4] {4} ; 737 \node[chiffre, below left of=7] {7} ; 738 \node[chiffre, above left of=2] {2} ; 739 \node[chiffre, above left of=8] {8} ; 740 741 \draw[arr] (1) -- (5) ; 742 \draw[arr] (3) -- (8) ; 743 \draw[arr] (2) -- (6) ; 744 \draw[arr] (4) -- (7) ; 745 \end{tikzpicture} 746 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 747 \label{fig:clause-conting} 748 \end{figure} 749 \end{frame} 750 751 %Clause Contingente 18 - jc 752 \begin{frame} 753 \begin{figure}[h!] 754 \centering 755 \begin{tikzpicture}[ 756 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 757 lettre/.style={ 758 on chain, 759 draw, 760 circle, 761 minimum size=1cm 762 }, 763 chiffre/.style={ 764 node distance = 0.75cm 765 }, 766 arr/.style={ 767 ->, 768 >=triangle 90 769 } 770 ] 771 \node[lettre] (1) {$\lnot x1$} ; 772 \node[lettre] (5) {$x2$} ; 773 \node[lettre] (3) {$\lnot x2$} ; 774 \node[lettre] (6) {$x3$} ; 775 \node[lettre] (4) {$\lnot x3$} ; 776 \node[lettre] (7) {$x4$} ; 777 \node[lettre] (2) {$\lnot x4$} ; 778 \node[lettre] (8) {$x1$} ; 779 780 \node[right of=1] {\textcolor{red}{faux}} ; 781 \node[right of=6] {\textcolor{green!75!black}{vrai}} ; 782 \node[left of=7] {\textcolor{green!75!black}{vrai}} ; 783 \node[left of=2] {\textcolor{red}{faux}} ; 784 \node[left of=8] {\textcolor{green!75!black}{vrai}} ; 785 786 \node[chiffre, above right of=1] {1} ; 787 \node[chiffre, above right of=5] {5} ; 788 \node[chiffre, below right of=3] {3} ; 789 \node[chiffre, below right of=6] {6} ; 790 \node[chiffre, below left of=4] {4} ; 791 \node[chiffre, below left of=7] {7} ; 792 \node[chiffre, above left of=2] {2} ; 793 \node[chiffre, above left of=8] {8} ; 794 795 \draw[arr] (1) -- (5) ; 796 \draw[arr] (3) -- (8) ; 797 \draw[arr] (2) -- (6) ; 798 \draw[arr] (4) -- (7) ; 799 \end{tikzpicture} 800 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 801 \label{fig:clause-conting} 802 \end{figure} 803 \end{frame} 804 805 %Clause Contingente 19 - jc 806 \begin{frame} 807 \begin{figure}[h!] 808 \centering 809 \begin{tikzpicture}[ 810 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 811 lettre/.style={ 812 on chain, 813 draw, 814 circle, 815 minimum size=1cm 816 }, 817 chiffre/.style={ 818 node distance = 0.75cm 819 }, 820 arr/.style={ 821 ->, 822 >=triangle 90 823 } 824 ] 825 \node[lettre] (1) {$\lnot x1$} ; 826 \node[lettre] (5) {$x2$} ; 827 \node[lettre] (3) {$\lnot x2$} ; 828 \node[lettre] (6) {$x3$} ; 829 \node[lettre] (4) {$\lnot x3$} ; 830 \node[lettre] (7) {$x4$} ; 831 \node[lettre] (2) {$\lnot x4$} ; 832 \node[lettre] (8) {$x1$} ; 833 834 \node[right of=1] {\textcolor{red}{faux}} ; 835 \node[right of=6] {\textcolor{green!75!black}{vrai}} ; 836 \node[left of=4] {\textcolor{red}{faux}} ; 837 \node[left of=7] {\textcolor{green!75!black}{vrai}} ; 838 \node[left of=2] {\textcolor{red}{faux}} ; 839 \node[left of=8] {\textcolor{green!75!black}{vrai}} ; 840 841 \node[chiffre, above right of=1] {1} ; 842 \node[chiffre, above right of=5] {5} ; 843 \node[chiffre, below right of=3] {3} ; 844 \node[chiffre, below right of=6] {6} ; 845 \node[chiffre, below left of=4] {4} ; 846 \node[chiffre, below left of=7] {7} ; 847 \node[chiffre, above left of=2] {2} ; 848 \node[chiffre, above left of=8] {8} ; 849 850 \draw[arr] (1) -- (5) ; 851 \draw[arr] (3) -- (8) ; 852 \draw[arr] (2) -- (6) ; 853 \draw[arr] (4) -- (7) ; 854 \end{tikzpicture} 855 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 856 \label{fig:clause-conting} 857 \end{figure} 858 \end{frame} 859 860 %Clause Contingente 20 - jc 861 \begin{frame} 862 \begin{figure}[h!] 863 \centering 864 \begin{tikzpicture}[ 865 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 866 lettre/.style={ 867 on chain, 868 draw, 869 circle, 870 minimum size=1cm 871 }, 872 chiffre/.style={ 873 node distance = 0.75cm 874 }, 875 arr/.style={ 876 ->, 877 >=triangle 90 878 } 879 ] 880 \node[lettre] (1) {$\lnot x1$} ; 881 \node[lettre] (5) {$x2$} ; 882 \node[lettre] (3) {$\lnot x2$} ; 883 \node[lettre] (6) {$x3$} ; 884 \node[lettre] (4) {$\lnot x3$} ; 885 \node[lettre] (7) {$x4$} ; 886 \node[lettre] (2) {$\lnot x4$} ; 887 \node[lettre] (8) {$x1$} ; 888 889 \node[right of=1] {\textcolor{red}{faux}} ; 890 \node[right of=5] {\textcolor{green!75!black}{vrai}} ; 891 \node[right of=6] {\textcolor{green!75!black}{vrai}} ; 892 \node[left of=4] {\textcolor{red}{faux}} ; 893 \node[left of=7] {\textcolor{green!75!black}{vrai}} ; 894 \node[left of=2] {\textcolor{red}{faux}} ; 895 \node[left of=8] {\textcolor{green!75!black}{vrai}} ; 896 897 \node[chiffre, above right of=1] {1} ; 898 \node[chiffre, above right of=5] {5} ; 899 \node[chiffre, below right of=3] {3} ; 900 \node[chiffre, below right of=6] {6} ; 901 \node[chiffre, below left of=4] {4} ; 902 \node[chiffre, below left of=7] {7} ; 903 \node[chiffre, above left of=2] {2} ; 904 \node[chiffre, above left of=8] {8} ; 905 906 \draw[arr] (1) -- (5) ; 907 \draw[arr] (3) -- (8) ; 908 \draw[arr] (2) -- (6) ; 909 \draw[arr] (4) -- (7) ; 910 \end{tikzpicture} 911 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 912 \label{fig:clause-conting} 913 \end{figure} 914 \end{frame} 915 916 %Clause Contingente 21 - jc 917 \begin{frame} 918 \begin{figure}[h!] 919 \centering 920 \begin{tikzpicture}[ 921 start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)}, 922 lettre/.style={ 923 on chain, 924 draw, 925 circle, 926 minimum size=1cm 927 }, 928 chiffre/.style={ 929 node distance = 0.75cm 930 }, 931 arr/.style={ 932 ->, 933 >=triangle 90 934 } 935 ] 936 \node[lettre] (1) {$\lnot x1$} ; 937 \node[lettre] (5) {$x2$} ; 938 \node[lettre] (3) {$\lnot x2$} ; 939 \node[lettre] (6) {$x3$} ; 940 \node[lettre] (4) {$\lnot x3$} ; 941 \node[lettre] (7) {$x4$} ; 942 \node[lettre] (2) {$\lnot x4$} ; 943 \node[lettre] (8) {$x1$} ; 944 945 \node[right of=1] {\textcolor{red}{faux}} ; 946 \node[right of=5] {\textcolor{green!75!black}{vrai}} ; 947 \node[right of=3] {\textcolor{red}{faux}} ; 948 \node[right of=6] {\textcolor{green!75!black}{vrai}} ; 949 \node[left of=4] {\textcolor{red}{faux}} ; 950 \node[left of=7] {\textcolor{green!75!black}{vrai}} ; 951 \node[left of=2] {\textcolor{red}{faux}} ; 952 \node[left of=8] {\textcolor{green!75!black}{vrai}} ; 953 954 \node[chiffre, above right of=1] {1} ; 955 \node[chiffre, above right of=5] {5} ; 956 \node[chiffre, below right of=3] {3} ; 957 \node[chiffre, below right of=6] {6} ; 958 \node[chiffre, below left of=4] {4} ; 959 \node[chiffre, below left of=7] {7} ; 960 \node[chiffre, above left of=2] {2} ; 961 \node[chiffre, above left of=8] {8} ; 962 963 \draw[arr] (1) -- (5) ; 964 \draw[arr] (3) -- (8) ; 965 \draw[arr] (2) -- (6) ; 966 \draw[arr] (4) -- (7) ; 967 \end{tikzpicture} 968 \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$} 969 \label{fig:clause-conting} 970 \end{figure} 971 \end{frame} 972 973 %Clause Valide 01 - jc 974 \begin{frame} 975 \begin{figure}[h!] 976 \centering 977 \begin{tikzpicture}[ 978 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 979 lettre/.style={ 980 on chain, 981 draw, 982 circle, 983 minimum size=1cm 984 }, 985 chiffre/.style={ 986 node distance = 0.75cm 987 }, 988 arr/.style={ 989 ->, 990 >=triangle 90 991 } 992 ] 993 \node[lettre] (1) {$\lnot x1$} ; 994 \node[lettre] (2) {$x1$} ; 995 \node[lettre] (3) {$\lnot x2$} ; 996 \node[lettre] (4) {$x2$} ; 997 998 \end{tikzpicture} 999 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1000 \label{fig:clause-valide} 1001 \end{figure} 1002 \end{frame} 1003 1004 %Clause Valide 02 - jc 1005 \begin{frame} 1006 \begin{figure}[h!] 1007 \centering 1008 \begin{tikzpicture}[ 1009 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 1010 lettre/.style={ 1011 on chain, 1012 draw, 1013 circle, 1014 minimum size=1cm 1015 }, 1016 chiffre/.style={ 1017 node distance = 0.75cm 1018 }, 1019 arr/.style={ 1020 ->, 1021 >=triangle 90 1022 } 1023 ] 1024 \node[lettre] (1) {$\lnot x1$} ; 1025 \node[lettre] (2) {$x1$} ; 1026 \node[lettre] (3) {$\lnot x2$} ; 1027 \node[lettre] (4) {$x2$} ; 1028 1029 \path 1030 (1) edge[loop above] (1) ; 1031 \end{tikzpicture} 1032 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1033 \label{fig:clause-valide} 1034 \end{figure} 1035 \end{frame} 1036 1037 1038 %Clause Valide 03 - jc 1039 \begin{frame} 1040 \begin{figure}[h!] 1041 \centering 1042 \begin{tikzpicture}[ 1043 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 1044 lettre/.style={ 1045 on chain, 1046 draw, 1047 circle, 1048 minimum size=1cm 1049 }, 1050 chiffre/.style={ 1051 node distance = 0.75cm 1052 }, 1053 arr/.style={ 1054 ->, 1055 >=triangle 90 1056 } 1057 ] 1058 \node[lettre] (1) {$\lnot x1$} ; 1059 \node[lettre] (2) {$x1$} ; 1060 \node[lettre] (3) {$\lnot x2$} ; 1061 \node[lettre] (4) {$x2$} ; 1062 1063 \path 1064 (1) edge[loop above] (1) 1065 (2) edge[loop above] (2) ; 1066 \end{tikzpicture} 1067 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1068 \label{fig:clause-valide} 1069 \end{figure} 1070 \end{frame} 1071 1072 1073 %Clause Valide 04 - jc 1074 \begin{frame} 1075 \begin{figure}[h!] 1076 \centering 1077 \begin{tikzpicture}[ 1078 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 1079 lettre/.style={ 1080 on chain, 1081 draw, 1082 circle, 1083 minimum size=1cm 1084 }, 1085 chiffre/.style={ 1086 node distance = 0.75cm 1087 }, 1088 arr/.style={ 1089 ->, 1090 >=triangle 90 1091 } 1092 ] 1093 \node[lettre] (1) {$\lnot x1$} ; 1094 \node[lettre] (2) {$x1$} ; 1095 \node[lettre] (3) {$\lnot x2$} ; 1096 \node[lettre] (4) {$x2$} ; 1097 1098 \path 1099 (1) edge[loop above] (1) 1100 (2) edge[loop above] (2) 1101 (3) edge[loop below] (3) ; 1102 \end{tikzpicture} 1103 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1104 \label{fig:clause-valide} 1105 \end{figure} 1106 \end{frame} 1107 1108 1109 %Clause Valide 05 - jc 1110 \begin{frame} 1111 \begin{figure}[h!] 1112 \centering 1113 \begin{tikzpicture}[ 1114 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 1115 lettre/.style={ 1116 on chain, 1117 draw, 1118 circle, 1119 minimum size=1cm 1120 }, 1121 chiffre/.style={ 1122 node distance = 0.75cm 1123 }, 1124 arr/.style={ 1125 ->, 1126 >=triangle 90 1127 } 1128 ] 1129 \node[lettre] (1) {$\lnot x1$} ; 1130 \node[lettre] (2) {$x1$} ; 1131 \node[lettre] (3) {$\lnot x2$} ; 1132 \node[lettre] (4) {$x2$} ; 1133 1134 \path 1135 (1) edge[loop above] (1) 1136 (2) edge[loop above] (2) 1137 (3) edge[loop below] (3) 1138 (4) edge[loop above] (4) ; 1139 \end{tikzpicture} 1140 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1141 \label{fig:clause-valide} 1142 \end{figure} 1143 \end{frame} 1144 1145 1146 %Clause Valide 06 - jc 1147 \begin{frame} 1148 \begin{figure}[h!] 1149 \centering 1150 \begin{tikzpicture}[ 1151 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 1152 lettre/.style={ 1153 on chain, 1154 draw, 1155 circle, 1156 minimum size=1cm 1157 }, 1158 chiffre/.style={ 1159 node distance = 0.75cm 1160 }, 1161 arr/.style={ 1162 ->, 1163 >=triangle 90 1164 } 1165 ] 1166 \node[lettre] (1) {$\lnot x1$} ; 1167 \node[lettre] (2) {$x1$} ; 1168 \node[lettre] (3) {$\lnot x2$} ; 1169 \node[lettre] (4) {$x2$} ; 1170 1171 \node[chiffre, above right of=1] {1} ; 1172 1173 \path 1174 (1) edge[loop above] (1) 1175 (2) edge[loop above] (2) 1176 (3) edge[loop below] (3) 1177 (4) edge[loop above] (4) ; 1178 \end{tikzpicture} 1179 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1180 \label{fig:clause-valide} 1181 \end{figure} 1182 \end{frame} 1183 1184 1185 %Clause Valide 07 - jc 1186 \begin{frame} 1187 \begin{figure}[h!] 1188 \centering 1189 \begin{tikzpicture}[ 1190 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 1191 lettre/.style={ 1192 on chain, 1193 draw, 1194 circle, 1195 minimum size=1cm 1196 }, 1197 chiffre/.style={ 1198 node distance = 0.75cm 1199 }, 1200 arr/.style={ 1201 ->, 1202 >=triangle 90 1203 } 1204 ] 1205 \node[lettre] (1) {$\lnot x1$} ; 1206 \node[lettre] (2) {$x1$} ; 1207 \node[lettre] (3) {$\lnot x2$} ; 1208 \node[lettre] (4) {$x2$} ; 1209 1210 \node[chiffre, above right of=1] {1} ; 1211 \node[chiffre, below right of=2] {2} ; 1212 1213 \path 1214 (1) edge[loop above] (1) 1215 (2) edge[loop above] (2) 1216 (3) edge[loop below] (3) 1217 (4) edge[loop above] (4) ; 1218 \end{tikzpicture} 1219 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1220 \label{fig:clause-valide} 1221 \end{figure} 1222 \end{frame} 1223 1224 1225 1226 1227 %Clause Valide 08 - jc 1228 \begin{frame} 1229 \begin{figure}[h!] 1230 \centering 1231 \begin{tikzpicture}[ 1232 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 1233 lettre/.style={ 1234 on chain, 1235 draw, 1236 circle, 1237 minimum size=1cm 1238 }, 1239 chiffre/.style={ 1240 node distance = 0.75cm 1241 }, 1242 arr/.style={ 1243 ->, 1244 >=triangle 90 1245 } 1246 ] 1247 \node[lettre] (1) {$\lnot x1$} ; 1248 \node[lettre] (2) {$x1$} ; 1249 \node[lettre] (3) {$\lnot x2$} ; 1250 \node[lettre] (4) {$x2$} ; 1251 1252 \node[chiffre, above right of=1] {1} ; 1253 \node[chiffre, below right of=2] {2} ; 1254 \node[chiffre, below right of=3] {3} ; 1255 1256 \path 1257 (1) edge[loop above] (1) 1258 (2) edge[loop above] (2) 1259 (3) edge[loop below] (3) 1260 (4) edge[loop above] (4) ; 1261 \end{tikzpicture} 1262 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1263 \label{fig:clause-valide} 1264 \end{figure} 1265 \end{frame} 1266 1267 %Clause Valide 09 - jc 1268 \begin{frame} 1269 \begin{figure}[h!] 1270 \centering 1271 \begin{tikzpicture}[ 1272 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 1273 lettre/.style={ 1274 on chain, 1275 draw, 1276 circle, 1277 minimum size=1cm 1278 }, 1279 chiffre/.style={ 1280 node distance = 0.75cm 1281 }, 1282 arr/.style={ 1283 ->, 1284 >=triangle 90 1285 } 1286 ] 1287 \node[lettre] (1) {$\lnot x1$} ; 1288 \node[lettre] (2) {$x1$} ; 1289 \node[lettre] (3) {$\lnot x2$} ; 1290 \node[lettre] (4) {$x2$} ; 1291 1292 \node[chiffre, above right of=1] {1} ; 1293 \node[chiffre, below right of=2] {2} ; 1294 \node[chiffre, below right of=3] {3} ; 1295 \node[chiffre, below left of=4] {4} ; 1296 1297 \path 1298 (1) edge[loop above] (1) 1299 (2) edge[loop above] (2) 1300 (3) edge[loop below] (3) 1301 (4) edge[loop above] (4) ; 1302 \end{tikzpicture} 1303 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1304 \label{fig:clause-valide} 1305 \end{figure} 1306 \end{frame} 1307 1308 1309 %Clause Valide 10 - jc 1310 \begin{frame} 1311 \begin{figure}[h!] 1312 \centering 1313 \begin{tikzpicture}[ 1314 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 1315 lettre/.style={ 1316 on chain, 1317 draw, 1318 circle, 1319 minimum size=1cm 1320 }, 1321 chiffre/.style={ 1322 node distance = 0.75cm 1323 }, 1324 arr/.style={ 1325 ->, 1326 >=triangle 90 1327 } 1328 ] 1329 \node[lettre] (1) {$\lnot x1$} ; 1330 \node[lettre] (2) {$x1$} ; 1331 \node[lettre] (3) {$\lnot x2$} ; 1332 \node[lettre] (4) {$x2$} ; 1333 1334 \node[left of=4] {\textcolor{green!75!black}{vrai}} ; 1335 1336 \node[chiffre, above right of=1] {1} ; 1337 \node[chiffre, below right of=2] {2} ; 1338 \node[chiffre, below right of=3] {3} ; 1339 \node[chiffre, below left of=4] {4} ; 1340 1341 \path 1342 (1) edge[loop above] (1) 1343 (2) edge[loop above] (2) 1344 (3) edge[loop below] (3) 1345 (4) edge[loop above] (4) ; 1346 \end{tikzpicture} 1347 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1348 \label{fig:clause-valide} 1349 \end{figure} 1350 \end{frame} 1351 1352 1353 %Clause Valide 11 - jc 1354 \begin{frame} 1355 \begin{figure}[h!] 1356 \centering 1357 \begin{tikzpicture}[ 1358 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 1359 lettre/.style={ 1360 on chain, 1361 draw, 1362 circle, 1363 minimum size=1cm 1364 }, 1365 chiffre/.style={ 1366 node distance = 0.75cm 1367 }, 1368 arr/.style={ 1369 ->, 1370 >=triangle 90 1371 } 1372 ] 1373 \node[lettre] (1) {$\lnot x1$} ; 1374 \node[lettre] (2) {$x1$} ; 1375 \node[lettre] (3) {$\lnot x2$} ; 1376 \node[lettre] (4) {$x2$} ; 1377 1378 \node[right of=3] {\textcolor{red}{faux}} ; 1379 \node[left of=4] {\textcolor{green!75!black}{vrai}} ; 1380 1381 \node[chiffre, above right of=1] {1} ; 1382 \node[chiffre, below right of=2] {2} ; 1383 \node[chiffre, below right of=3] {3} ; 1384 \node[chiffre, below left of=4] {4} ; 1385 1386 \path 1387 (1) edge[loop above] (1) 1388 (2) edge[loop above] (2) 1389 (3) edge[loop below] (3) 1390 (4) edge[loop above] (4) ; 1391 \end{tikzpicture} 1392 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1393 \label{fig:clause-valide} 1394 \end{figure} 1395 \end{frame} 1396 1397 1398 %Clause Valide 12 - jc 1399 \begin{frame} 1400 \begin{figure}[h!] 1401 \centering 1402 \begin{tikzpicture}[ 1403 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 1404 lettre/.style={ 1405 on chain, 1406 draw, 1407 circle, 1408 minimum size=1cm 1409 }, 1410 chiffre/.style={ 1411 node distance = 0.75cm 1412 }, 1413 arr/.style={ 1414 ->, 1415 >=triangle 90 1416 } 1417 ] 1418 \node[lettre] (1) {$\lnot x1$} ; 1419 \node[lettre] (2) {$x1$} ; 1420 \node[lettre] (3) {$\lnot x2$} ; 1421 \node[lettre] (4) {$x2$} ; 1422 1423 \node[right of=2] {\textcolor{green!75!black}{vrai}}; 1424 \node[right of=3] {\textcolor{red}{faux}} ; 1425 \node[left of=4] {\textcolor{green!75!black}{vrai}} ; 1426 1427 \node[chiffre, above right of=1] {1} ; 1428 \node[chiffre, below right of=2] {2} ; 1429 \node[chiffre, below right of=3] {3} ; 1430 \node[chiffre, below left of=4] {4} ; 1431 1432 \path 1433 (1) edge[loop above] (1) 1434 (2) edge[loop above] (2) 1435 (3) edge[loop below] (3) 1436 (4) edge[loop above] (4) ; 1437 \end{tikzpicture} 1438 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1439 \label{fig:clause-valide} 1440 \end{figure} 1441 \end{frame} 1442 1443 1444 %Clause Valide 13 - jc 1445 \begin{frame} 1446 \begin{figure}[h!] 1447 \centering 1448 \begin{tikzpicture}[ 1449 start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)}, 1450 lettre/.style={ 1451 on chain, 1452 draw, 1453 circle, 1454 minimum size=1cm 1455 }, 1456 chiffre/.style={ 1457 node distance = 0.75cm 1458 }, 1459 arr/.style={ 1460 ->, 1461 >=triangle 90 1462 } 1463 ] 1464 \node[lettre] (1) {$\lnot x1$} ; 1465 \node[lettre] (2) {$x1$} ; 1466 \node[lettre] (3) {$\lnot x2$} ; 1467 \node[lettre] (4) {$x2$} ; 1468 1469 \node[right of=1] {\textcolor{red}{faux}} ; 1470 \node[right of=2] {\textcolor{green!75!black}{vrai}}; 1471 \node[right of=3] {\textcolor{red}{faux}} ; 1472 \node[left of=4] {\textcolor{green!75!black}{vrai}} ; 1473 1474 \node[chiffre, above right of=1] {1} ; 1475 \node[chiffre, below right of=2] {2} ; 1476 \node[chiffre, below right of=3] {3} ; 1477 \node[chiffre, below left of=4] {4} ; 1478 1479 \path 1480 (1) edge[loop above] (1) 1481 (2) edge[loop above] (2) 1482 (3) edge[loop below] (3) 1483 (4) edge[loop above] (4) ; 1484 \end{tikzpicture} 1485 \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$} 1486 \label{fig:clause-valide} 1487 \end{figure} 1488 \end{frame} 1489 1490 % clause insatisfiable 01 - jc 1491 \begin{frame} 1492 \begin{figure}[h!] 1493 \centering 1494 \begin{tikzpicture}[ 1495 node distance=2.5cm, 1496 lettre/.style={ 1497 draw, 1498 circle, 1499 minimum size=1cm 1500 } 1501 ] 1502 \node[lettre] (nx1) {$\lnot x_1$} ; 1503 \node[lettre, below of=nx1] (x1) {$x_1$} ; 1504 \node[coordinate,xshift=0.1cm] (x1r) at (x1.north) {}; 1505 \node[coordinate,xshift=-0.1cm] (x1l) at (x1.north) {}; 1506 \node[coordinate,xshift=0.1cm] (nx1r) at (nx1.south) {}; 1507 \node[coordinate,xshift=-0.1cm] (nx1l) at (nx1.south) {}; 1508 1509 \end{tikzpicture} 1510 \caption{Clause insatisfiable : $(x_{1} \vee x_{1}) \wedge (\neg x_{1} \vee \neg x_{1})$} 1511 \label{fig:clause-insat} 1512 \end{figure} 1513 \end{frame} 1514 1515 % clause insatisfiable 02 - jc 1516 \begin{frame} 1517 \begin{figure}[h!] 1518 \centering 1519 \begin{tikzpicture}[ 1520 node distance=2.5cm, 1521 lettre/.style={ 1522 draw, 1523 circle, 1524 minimum size=1cm 1525 } 1526 ] 1527 \node[lettre] (nx1) {$\lnot x_1$} ; 1528 \node[lettre, below of=nx1] (x1) {$x_1$} ; 1529 \node[coordinate,xshift=0.1cm] (x1r) at (x1.north) {}; 1530 \node[coordinate,xshift=-0.1cm] (x1l) at (x1.north) {}; 1531 \node[coordinate,xshift=0.1cm] (nx1r) at (nx1.south) {}; 1532 \node[coordinate,xshift=-0.1cm] (nx1l) at (nx1.south) {}; 1533 \draw[->] (nx1l) -- (x1l); 1534 1535 \end{tikzpicture} 1536 \caption{Clause insatisfiable : $(x_{1} \vee x_{1}) \wedge (\neg x_{1} \vee \neg x_{1})$} 1537 \label{fig:clause-insat} 1538 \end{figure} 1539 \end{frame} 1540 1541 % clause insatisfiable 03 - jc 1542 \begin{frame} 1543 \begin{figure}[h!] 1544 \centering 1545 \begin{tikzpicture}[ 1546 node distance=2.5cm, 1547 lettre/.style={ 1548 draw, 1549 circle, 1550 minimum size=1cm 1551 } 1552 ] 1553 \node[lettre] (nx1) {$\lnot x_1$} ; 1554 \node[lettre, below of=nx1] (x1) {$x_1$} ; 1555 \node[coordinate,xshift=0.1cm] (x1r) at (x1.north) {}; 1556 \node[coordinate,xshift=-0.1cm] (x1l) at (x1.north) {}; 1557 \node[coordinate,xshift=0.1cm] (nx1r) at (nx1.south) {}; 1558 \node[coordinate,xshift=-0.1cm] (nx1l) at (nx1.south) {}; 1559 \draw[->] (x1r) -- (nx1r); 1560 \draw[->] (nx1l) -- (x1l); 1561 \end{tikzpicture} 1562 \caption{Clause insatisfiable : $(x_{1} \vee x_{1}) \wedge (\neg x_{1} \vee \neg x_{1})$} 1563 \label{fig:clause-insat} 1564 \end{figure} 1565 \end{frame} 1566 1567 % clause insatisfiable 04 - jc 1568 \begin{frame} 1569 \begin{figure}[h!] 1570 \centering 1571 \begin{tikzpicture}[ 1572 node distance=2.5cm, 1573 lettre/.style={ 1574 draw, 1575 circle, 1576 minimum size=1cm 1577 } 1578 ] 1579 \node[lettre] (nx1) {$\lnot x_1$} ; 1580 \node[lettre, below of=nx1] (x1) {$x_1$} ; 1581 \node[coordinate,xshift=0.1cm] (x1r) at (x1.north) {}; 1582 \node[coordinate,xshift=-0.1cm] (x1l) at (x1.north) {}; 1583 \node[coordinate,xshift=0.1cm] (nx1r) at (nx1.south) {}; 1584 \node[coordinate,xshift=-0.1cm] (nx1l) at (nx1.south) {}; 1585 \draw[->] (x1r) -- (nx1r); 1586 \draw[->] (nx1l) -- (x1l); 1587 \path 1588 (x1) edge[loop below] (x1) 1589 (nx1) edge[loop above] (nx1) ; 1590 \end{tikzpicture} 1591 \caption{Clause insatisfiable : $(x_{1} \vee x_{1}) \wedge (\neg x_{1} \vee \neg x_{1})$} 1592 \label{fig:clause-insat} 1593 \end{figure} 1594 \end{frame}