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However, the converse of a statement with mutually inclusive terms remains true, given the truth of the original proposition. This is equivalent to saying that the converse of a definition is true. Thus, the statement "If I am a triangle, then I am a three-sided polygon" is logically equivalent to
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2442:"The original proposition is called the exposita; when converted, it is denominated the converse. Conversion is valid when, and only when, nothing is asserted in the converse which is not affirmed or implied in the exposita."
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proposition "All cats are mammals", the converse "All mammals are cats" is obviously false. However, the weaker statement "Some mammals are cats" is true. Logicians define conversion
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In practice, when determining the converse of a mathematical theorem, aspects of the antecedent may be taken as establishing context. That is, the converse of "Given P, if Q then R
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For example, consider the true statement "If I am a human, then I am mortal." The converse of that statement is "If I am mortal, then I am a human," which is not necessarily
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1355:"If I am a three-sided polygon, then I am a triangle," because the definition of "triangle" is "three-sided polygon".
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2662:. It is therefore clear that the categorical converse is closely related to the implicational converse, and that
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of a categorical or implicational statement is the result of reversing its two constituent statements. For the
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The "exposita" is more usually called the "convertend". In its simple form, conversion is valid only for
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to be the process of producing this weaker statement. Inference from a statement to its converse
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statement to its converse is not valid. As an example, for the
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was proved in 1912, but its converse was proved only in 1997.
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The
Science of Logic: or, An Analysis of the Laws of Thought
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is also true), then affirming the consequent will be valid.
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Going from a statement to its converse is the fallacy of
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says nothing about the truth of its converse, unless the
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In mathematics, the converse of a theorem of the form
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2764:"What Are the Converse, Contrapositive, and Inverse?"
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Reverse of a categorical or hypothetical proposition
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The World and
Language in Wittgenstein's Philosophy
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2853:William Thomas Parry and Edward A. Hacker (1991),
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2003:(Book I, Proposition 48), can be stated as:
2547:The validity of simple conversion only for
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2789:"The Four Vertex Theorem and its Converse"
2305:{\displaystyle R^{T}=\{(b,a):(a,b)\in R\}}
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2410:Categorical proposition § Conversion
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2171:Converse a simple mathematical relation
1536:and its converse are equivalent (i.e.,
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518:{\displaystyle A\not \Leftrightarrow B}
21:
2750:The Cambridge Dictionary of Philosophy
2655:{\displaystyle \forall x.S(x)\to P(x)}
2136:the angle opposite the side of length
1912:the angle opposite the side of length
945:{\displaystyle A{\underline {\lor }}B}
460:{\displaystyle {\overline {A\cdot B}}}
373:{\displaystyle A{\overline {\land }}B}
3202:{\displaystyle \not \leftrightarrow }
2590:is generally valid. However, as with
2227:{\displaystyle R\subseteq A\times B,}
585:{\displaystyle A{\overline {\lor }}B}
246:{\displaystyle A\leftrightharpoons B}
7:
2787:Shonkwiler, Clay (October 6, 2006).
1996:The converse, which also appears in
904:{\displaystyle A\ {\text{XNOR}}\ B}
544:{\displaystyle A\nleftrightarrow B}
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2931:. MacMillan, 1979, fifth edition.
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1358:A truth table makes it clear that
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220:{\displaystyle A\Leftrightarrow B}
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14:
2125:{\displaystyle a^{2}+b^{2}=c^{2}}
1983:{\displaystyle a^{2}+b^{2}=c^{2}}
646:{\displaystyle {\overline {A+B}}}
3414:
3231:{\displaystyle \leftrightarrow }
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2324:The converse of the implication
2010:a triangle with sides of length
1842:a triangle with sides of length
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1746:
1736:{\displaystyle \Leftrightarrow }
1716:
1638:{\displaystyle \Leftrightarrow }
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727:{\displaystyle {\overline {A}}}
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2939:A Modern Introduction to Logic
2817:& Thomas Ströhlein (1993)
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2603:first-order predicate calculus
2418:. For example, going from "No
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1432:{\displaystyle P\rightarrow Q}
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492:{\displaystyle A\not \equiv B}
390:
332:{\displaystyle A\rightarrow B}
323:
280:{\displaystyle A\Rightarrow B}
271:
237:
211:
160:{\displaystyle A\&\&B}
1:
3307:{\displaystyle \nrightarrow }
2877:, C. Scribner's sons, p. 156.
2359:{\displaystyle P\leftarrow Q}
1827:will be "Given P, if R then Q
1616:{\displaystyle P\leftarrow Q}
1459:{\displaystyle P\leftarrow Q}
1276:{\displaystyle P\leftarrow Q}
1057:{\displaystyle A\leftarrow B}
1005:{\displaystyle A\Leftarrow B}
611:{\displaystyle A\downarrow B}
3332:{\displaystyle \nleftarrow }
3107:{\displaystyle \rightarrow }
1532:. However, if the statement
1326:). In general, the truth of
862:{\displaystyle A\parallel B}
719:
638:
574:
452:
362:
3278:{\displaystyle \downarrow }
3078:{\displaystyle \leftarrow }
1294:be a statement of the form
399:{\displaystyle A\uparrow B}
3461:
2567:propositions, neither is.
2407:
2385:{\displaystyle P\subset Q}
2366:, but may also be notated
1344:are logically equivalent.
1031:{\displaystyle A\subset B}
306:{\displaystyle A\supset B}
3411:
3374:
3254:
3149:
3053:{\displaystyle \uparrow }
3029:
3018:
2983:
2941:. Cromwell Company, 1931.
2748:Robert Audi, ed. (1999),
971:{\displaystyle A\oplus B}
194:{\displaystyle A\equiv B}
2886:Gordon Hunnings (1988),
1530:affirming the consequent
131:{\displaystyle A\&B}
82:{\displaystyle A\cdot B}
56:{\displaystyle A\land B}
3317:Converse nonimplication
1233:categorical proposition
1111:Functional completeness
836:{\displaystyle A\mid B}
784:{\displaystyle A\lor B}
425:{\displaystyle A\mid B}
3399:
3362:
3361:{\displaystyle \land }
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2163:Converse of a relation
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1705:{\displaystyle \neg Q}
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1586:{\displaystyle \neg Q}
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1246:Implicational converse
1081:Propositional calculus
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750:{\displaystyle \sim A}
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3421:Philosophy portal
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3398:{\displaystyle \bot }
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3173:{\displaystyle \neg }
3138:
3136:{\displaystyle \lor }
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3007:{\displaystyle \top }
2922:Introduction to Logic
2875:The Elements of Logic
2730:Transposition (logic)
2670:cannot be swapped in
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1796:Converse of a theorem
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1765:{\displaystyle \lor }
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1139:Programming languages
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3063:Converse implication
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2819:Relations and Graphs
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2473:(valid if P exists)
2426:to its converse "No
2404:Categorical converse
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3445:Immediate inference
3440:Logical connectives
2977:logical connectives
2924:. MacMillan, 1953.
2312:is also called the
1833:Pythagorean theorem
1831:. For example, the
1818:four-vertex theorem
1149:Philosophy of logic
810:{\displaystyle A+B}
23:Logical connectives
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3034:Alternative denial
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2855:Aristotelian Logic
2796:math.colostate.edu
2762:Taylor, Courtney.
2715:Logical connective
2652:
2434:. In the words of
2398:Bocheński notation
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2158:is a right angle.
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1934:is a right angle,
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1238:, the converse is
1223:, the converse is
1144:Mathematical logic
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700:{\displaystyle -A}
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105:{\displaystyle AB}
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2692:Philosophy portal
2545:
2544:
2236:converse relation
2188:{\displaystyle R}
2150:{\displaystyle c}
2068:{\displaystyle c}
2046:{\displaystyle b}
2024:{\displaystyle a}
1926:{\displaystyle c}
1900:{\displaystyle c}
1878:{\displaystyle b}
1856:{\displaystyle a}
1782:
1781:
1660:{\displaystyle P}
1563:{\displaystyle P}
1526:
1525:
1405:{\displaystyle Q}
1384:{\displaystyle P}
1314:is the statement
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2507:Some P is not S
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1106:Boolean function
1072:Related concepts
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1055:
1037:
1035:
1034:
1029:
1011:
1009:
1008:
1003:
977:
975:
974:
969:
951:
949:
948:
943:
938:
910:
908:
907:
902:
895:
894:
891:
887:
868:
866:
865:
860:
842:
840:
839:
834:
816:
814:
813:
808:
790:
788:
787:
782:
756:
754:
753:
748:
733:
731:
730:
725:
723:
715:
706:
704:
703:
698:
683:
681:
680:
675:
652:
650:
649:
644:
642:
637:
626:
617:
615:
614:
609:
591:
589:
588:
583:
578:
570:
550:
548:
547:
542:
524:
522:
521:
516:
498:
496:
495:
490:
466:
464:
463:
458:
456:
451:
440:
431:
429:
428:
423:
405:
403:
402:
397:
379:
377:
376:
371:
366:
358:
338:
336:
335:
330:
312:
310:
309:
304:
286:
284:
283:
278:
252:
250:
249:
244:
226:
224:
223:
218:
200:
198:
197:
192:
166:
164:
163:
158:
137:
135:
134:
129:
111:
109:
108:
103:
88:
86:
85:
80:
62:
60:
59:
54:
30:
29:
19:
3460:
3459:
3455:
3454:
3453:
3451:
3450:
3449:
3430:
3429:
3428:
3423:
3415:
3413:
3407:
3387:
3386:
3370:
3350:
3349:
3321:
3320:
3296:
3295:
3267:
3266:
3250:
3220:
3219:
3191:
3190:
3162:
3161:
3145:
3125:
3124:
3096:
3095:
3067:
3066:
3042:
3041:
3025:
3016:
2996:
2995:
2979:
2973:
2935:Stebbing, Susan
2904:
2902:Further reading
2899:
2898:
2885:
2881:
2871:James H. Hyslop
2869:
2865:
2852:
2848:
2832:
2828:
2815:Gunther Schmidt
2813:
2809:
2800:
2798:
2791:
2786:
2785:
2781:
2772:
2770:
2761:
2760:
2756:
2747:
2743:
2738:
2710:Inverse (logic)
2690:
2685:
2683:
2680:
2611:
2610:
2533:Some S is not P
2466:Simple converse
2412:
2406:
2368:
2367:
2342:
2341:
2332:may be written
2322:
2244:
2239:
2238:
2201:
2200:
2197:binary relation
2177:
2176:
2165:
2139:
2138:
2112:
2099:
2086:
2081:
2080:
2057:
2056:
2035:
2034:
2013:
2012:
1970:
1957:
1944:
1939:
1938:
1915:
1914:
1889:
1888:
1867:
1866:
1845:
1844:
1798:
1754:
1753:
1743:
1725:
1724:
1691:
1690:
1670:
1669:
1649:
1648:
1645:
1627:
1626:
1599:
1598:
1572:
1571:
1552:
1551:
1442:
1441:
1415:
1414:
1394:
1393:
1373:
1372:
1283:
1259:
1258:
1248:
1194:
1153:
1120:
1091:Boolean algebra
1086:Predicate logic
1040:
1039:
1014:
1013:
988:
987:
954:
953:
921:
920:
879:
878:
845:
844:
819:
818:
793:
792:
767:
766:
736:
735:
709:
708:
686:
685:
663:
662:
627:
620:
619:
594:
593:
561:
560:
527:
526:
501:
500:
475:
474:
441:
434:
433:
408:
407:
382:
381:
349:
348:
315:
314:
289:
288:
263:
262:
229:
228:
203:
202:
177:
176:
140:
139:
114:
113:
91:
90:
65:
64:
39:
38:
17:
12:
11:
5:
3458:
3456:
3448:
3447:
3442:
3432:
3431:
3425:
3424:
3412:
3409:
3408:
3406:
3405:
3394:
3375:
3372:
3371:
3369:
3368:
3357:
3339:
3328:
3314:
3303:
3288:Nonimplication
3285:
3274:
3255:
3252:
3251:
3249:
3248:
3245:Digital buffer
3238:
3227:
3209:
3198:
3180:
3169:
3150:
3147:
3146:
3144:
3143:
3132:
3114:
3103:
3085:
3074:
3060:
3049:
3030:
3027:
3026:
3019:
3017:
3015:
3014:
3003:
2984:
2981:
2980:
2974:
2972:
2971:
2964:
2957:
2949:
2943:
2942:
2932:
2929:Symbolic Logic
2927:Copi, Irving.
2925:
2915:
2903:
2900:
2897:
2896:
2890:, SUNY Press,
2879:
2863:
2857:, SUNY Press,
2846:
2826:
2823:Springer books
2807:
2779:
2754:
2740:
2739:
2737:
2734:
2733:
2732:
2727:
2722:
2717:
2712:
2707:
2705:Contraposition
2702:
2696:
2695:
2679:
2676:
2651:
2648:
2645:
2642:
2639:
2636:
2633:
2630:
2627:
2624:
2621:
2618:
2543:
2542:
2539:
2534:
2531:
2525:
2524:
2521:
2518:
2515:
2509:
2508:
2505:
2502:
2499:
2493:
2492:
2489:
2484:
2481:
2475:
2474:
2467:
2464:
2461:
2454:propositions:
2405:
2402:
2381:
2378:
2375:
2355:
2352:
2349:
2321:
2318:
2301:
2298:
2295:
2292:
2289:
2286:
2283:
2280:
2277:
2274:
2271:
2268:
2265:
2262:
2259:
2256:
2251:
2247:
2223:
2220:
2217:
2214:
2211:
2208:
2184:
2164:
2161:
2146:
2119:
2115:
2111:
2106:
2102:
2098:
2093:
2089:
2064:
2042:
2020:
1977:
1973:
1969:
1964:
1960:
1956:
1951:
1947:
1922:
1896:
1874:
1852:
1797:
1794:
1780:
1779:
1772:
1761:
1751:
1744:
1732:
1723:
1721:
1713:
1712:
1701:
1698:
1688:
1677:
1667:
1656:
1646:
1634:
1625:
1623:
1612:
1609:
1606:
1582:
1579:
1559:
1542:if and only if
1524:
1523:
1520:
1517:
1514:
1510:
1509:
1506:
1503:
1500:
1496:
1495:
1492:
1489:
1486:
1482:
1481:
1478:
1475:
1472:
1468:
1467:
1455:
1452:
1449:
1439:
1428:
1425:
1422:
1412:
1401:
1391:
1380:
1272:
1269:
1266:
1247:
1244:
1196:
1195:
1193:
1192:
1185:
1178:
1170:
1167:
1166:
1155:
1154:
1152:
1151:
1146:
1141:
1136:
1130:
1127:
1126:
1122:
1121:
1119:
1118:
1113:
1108:
1103:
1101:Truth function
1098:
1093:
1088:
1083:
1077:
1074:
1073:
1069:
1068:
1065:
1064:
1053:
1050:
1047:
1027:
1024:
1021:
1001:
998:
995:
985:
979:
978:
967:
964:
961:
941:
936:
933:
928:
918:
912:
911:
900:
886:
876:
870:
869:
858:
855:
852:
832:
829:
826:
806:
803:
800:
780:
777:
774:
764:
758:
757:
746:
743:
721:
718:
696:
693:
673:
670:
660:
654:
653:
640:
636:
633:
630:
607:
604:
601:
581:
576:
573:
568:
558:
552:
551:
540:
537:
534:
514:
511:
508:
488:
485:
482:
472:
468:
467:
454:
450:
447:
444:
421:
418:
415:
395:
392:
389:
369:
364:
361:
356:
346:
340:
339:
328:
325:
322:
302:
299:
296:
276:
273:
270:
260:
254:
253:
242:
239:
236:
216:
213:
210:
190:
187:
184:
174:
168:
167:
156:
153:
150:
147:
127:
124:
121:
101:
98:
78:
75:
72:
52:
49:
46:
36:
26:
25:
15:
13:
10:
9:
6:
4:
3:
2:
3457:
3446:
3443:
3441:
3438:
3437:
3435:
3422:
3410:
3384:
3380:
3379:Contradiction
3377:
3376:
3373:
3355:
3347:
3343:
3340:
3326:
3318:
3315:
3301:
3293:
3289:
3286:
3264:
3260:
3257:
3256:
3253:
3246:
3242:
3239:
3217:
3213:
3212:Biconditional
3210:
3196:
3188:
3184:
3181:
3159:
3155:
3152:
3151:
3148:
3130:
3122:
3118:
3115:
3093:
3089:
3086:
3064:
3061:
3039:
3035:
3032:
3031:
3028:
3023:
2993:
2989:
2986:
2985:
2982:
2978:
2970:
2965:
2963:
2958:
2956:
2951:
2950:
2947:
2940:
2936:
2933:
2930:
2926:
2923:
2919:
2916:
2913:
2909:
2906:
2905:
2901:
2893:
2889:
2883:
2880:
2876:
2872:
2867:
2864:
2860:
2856:
2850:
2847:
2843:
2839:
2835:
2830:
2827:
2824:
2820:
2816:
2811:
2808:
2797:
2790:
2783:
2780:
2769:
2765:
2758:
2755:
2751:
2745:
2742:
2735:
2731:
2728:
2726:
2723:
2721:
2718:
2716:
2713:
2711:
2708:
2706:
2703:
2701:
2698:
2697:
2693:
2682:
2677:
2675:
2673:
2669:
2665:
2646:
2640:
2631:
2625:
2622:
2619:
2608:
2604:
2599:
2597:
2593:
2589:
2585:
2581:
2577:
2573:
2568:
2566:
2562:
2558:
2554:
2550:
2540:
2538:
2535:
2532:
2530:
2527:
2526:
2522:
2519:
2516:
2514:
2511:
2510:
2506:
2503:
2500:
2498:
2495:
2494:
2490:
2488:
2485:
2482:
2480:
2477:
2476:
2472:
2468:
2465:
2462:
2459:
2458:
2455:
2453:
2449:
2443:
2439:
2437:
2433:
2429:
2425:
2421:
2417:
2411:
2403:
2401:
2399:
2395:
2379:
2376:
2373:
2353:
2347:
2339:
2335:
2331:
2327:
2319:
2317:
2315:
2296:
2293:
2287:
2284:
2281:
2275:
2269:
2266:
2263:
2254:
2249:
2245:
2237:
2221:
2218:
2215:
2212:
2209:
2206:
2198:
2182:
2169:
2162:
2159:
2157:
2144:
2135:
2117:
2113:
2109:
2104:
2100:
2096:
2091:
2087:
2079:
2075:
2062:
2053:
2040:
2031:
2018:
2009:
2004:
2002:
2001:
1993:
1992:
1975:
1971:
1967:
1962:
1958:
1954:
1949:
1945:
1937:
1933:
1920:
1911:
1907:
1894:
1885:
1872:
1863:
1850:
1841:
1836:
1834:
1830:
1826:
1821:
1819:
1815:
1811:
1807:
1803:
1795:
1793:
1791:
1787:
1777:
1773:
1759:
1752:
1749:
1745:
1722:
1719:
1715:
1714:
1699:
1689:
1675:
1668:
1654:
1647:
1624:
1610:
1604:
1597:
1596:
1593:
1580:
1557:
1548:
1546:
1543:
1539:
1535:
1531:
1521:
1518:
1515:
1512:
1511:
1507:
1504:
1501:
1498:
1497:
1493:
1490:
1487:
1484:
1483:
1479:
1476:
1473:
1470:
1469:
1453:
1447:
1426:
1420:
1399:
1392:
1378:
1371:
1370:
1367:
1365:
1361:
1356:
1352:
1350:
1345:
1343:
1340:
1336:
1333:
1329:
1325:
1321:
1317:
1313:
1309:
1305:
1301:
1297:
1293:
1270:
1264:
1256:
1252:
1245:
1243:
1241:
1237:
1234:
1230:
1226:
1222:
1218:
1215:
1211:
1207:
1203:
1191:
1186:
1184:
1179:
1177:
1172:
1171:
1169:
1168:
1165:
1157:
1156:
1150:
1147:
1145:
1142:
1140:
1137:
1135:
1134:Digital logic
1132:
1131:
1129:
1128:
1123:
1117:
1116:Scope (logic)
1114:
1112:
1109:
1107:
1104:
1102:
1099:
1097:
1094:
1092:
1089:
1087:
1084:
1082:
1079:
1078:
1076:
1075:
1070:
1051:
1045:
1025:
1022:
1019:
999:
993:
986:
984:
981:
980:
965:
962:
959:
939:
934:
931:
926:
919:
917:
914:
913:
898:
884:
877:
875:
872:
871:
856:
853:
850:
830:
827:
824:
804:
801:
798:
778:
775:
772:
765:
763:
760:
759:
744:
741:
716:
694:
691:
671:
661:
659:
656:
655:
634:
631:
628:
605:
599:
579:
571:
566:
559:
557:
554:
553:
538:
535:
532:
512:
509:
506:
486:
483:
480:
473:
471:nonequivalent
470:
469:
448:
445:
442:
419:
416:
413:
393:
387:
367:
359:
354:
347:
345:
342:
341:
326:
320:
300:
297:
294:
274:
268:
261:
259:
256:
255:
240:
234:
214:
208:
188:
185:
182:
175:
173:
170:
169:
154:
145:
125:
119:
99:
96:
76:
73:
70:
50:
47:
44:
37:
35:
32:
31:
28:
27:
24:
20:
3259:Joint denial
3183:Exclusive or
3062:
2938:
2928:
2921:
2918:Copi, Irving
2911:
2887:
2882:
2874:
2866:
2854:
2849:
2837:
2829:
2818:
2810:
2799:. Retrieved
2795:
2782:
2771:. Retrieved
2767:
2757:
2749:
2744:
2671:
2667:
2663:
2606:
2600:
2596:per accidens
2595:
2588:per accidens
2587:
2584:per accidens
2583:
2579:
2575:
2571:
2569:
2564:
2563:, while for
2556:
2552:
2548:
2546:
2536:
2528:
2512:
2496:
2491:Some P is S
2486:
2478:
2471:per accidens
2470:
2451:
2447:
2445:
2441:
2431:
2427:
2423:
2419:
2415:
2413:
2393:
2337:
2333:
2329:
2325:
2323:
2313:
2174:
2137:
2133:
2077:
2055:
2033:
2011:
2007:
2006:
1999:
1995:
1990:
1935:
1913:
1909:
1887:
1865:
1843:
1839:
1838:
1828:
1824:
1822:
1813:
1809:
1805:
1801:
1799:
1789:
1785:
1783:
1549:
1544:
1537:
1533:
1527:
1363:
1359:
1357:
1353:
1346:
1341:
1334:
1327:
1323:
1319:
1315:
1311:
1307:
1306:). Then the
1303:
1299:
1295:
1291:
1289:
1255:Venn diagram
1239:
1235:
1228:
1224:
1220:
1216:
1209:
1199:
1125:Applications
982:
3342:Conjunction
3292:NIMPLY gate
3117:Disjunction
3088:Implication
2672:All S are P
2607:All S are P
2561:distributed
2520:Some P is S
2517:Some S is P
2483:All S are P
1316:Q implies P
1296:P implies Q
1240:All P are S
1236:All S are P
1214:implication
1206:mathematics
1096:Truth table
3434:Categories
3092:IMPLY gate
2821:, page 9,
2801:2019-11-26
2773:2019-11-27
2736:References
2725:Term logic
2592:syllogisms
2463:Convertend
2416:conversion
2408:See also:
1466:(converse)
1339:consequent
1332:antecedent
1231:. For the
172:equivalent
3393:⊥
3356:∧
3327:↚
3302:↛
3273:↓
3241:Statement
3226:↔
3216:XNOR gate
3168:¬
3131:∨
3102:→
3073:←
3048:↑
3038:NAND gate
3002:⊤
2988:Tautology
2908:Aristotle
2834:Asa Mahan
2768:ThoughtCo
2720:Obversion
2700:Aristotle
2638:→
2617:∀
2537:not valid
2504:No P is S
2501:No S is P
2487:not valid
2469:Converse
2436:Asa Mahan
2377:⊂
2351:←
2314:transpose
2294:∈
2234:then the
2216:×
2210:⊆
1998:Euclid's
1760:∨
1731:⇔
1697:¬
1676:∨
1633:⇔
1608:←
1578:¬
1451:←
1424:→
1268:←
1049:←
1023:⊂
997:⇐
963:⊕
935:_
932:∨
854:∥
828:∣
776:∨
742:∼
720:¯
692:−
669:¬
639:¯
603:↓
575:¯
572:∨
536:↮
453:¯
446:⋅
417:∣
391:↑
363:¯
360:∧
324:→
298:⊃
272:⇒
238:⇋
212:⇔
186:≡
152:&
149:&
123:&
74:⋅
48:∧
3346:AND gate
3263:NOR gate
3197:↮
3187:XOR gate
3158:NOT gate
3154:Negation
2873:(1892),
2678:See also
2320:Notation
2000:Elements
1808:will be
1788:without
1540:is true
1337:and the
1308:converse
1210:converse
1164:Category
983:converse
510:⇎
484:≢
3348:)
3344: (
3294:)
3290: (
3265:)
3261: (
3243: (
3218:)
3214: (
3189:)
3185: (
3160:)
3156: (
3123:)
3121:OR gate
3119: (
3094:)
3090: (
3040:)
3036: (
2975:Common
2912:Organon
2836:(1857)
2392:, or "B
258:implies
3385:
3319:
3065:
2994:
2859:p. 207
2396:" (in
2054:, and
1886:, and
1208:, the
896:
888:
3383:False
2892:p. 42
2842:p. 82
2792:(PDF)
2199:with
2195:is a
2008:Given
1840:Given
1202:logic
2992:True
2666:and
2570:For
2551:and
2460:Type
2450:and
2430:are
2422:are
2134:then
1936:then
1570:and
1349:true
1290:Let
1204:and
892:XNOR
874:XNOR
344:NAND
2601:In
2400:).
2175:If
1792:".
1310:of
1257:of
1200:In
916:XOR
658:NOT
556:NOR
34:AND
3436::
2937:.
2920:.
2910:.
2840:,
2794:.
2766:.
2674:.
2605:,
2541:–
2523:–
2438::
2432:S"
2424:P"
2394:pq
2340:,
2336:→
2328:→
2316:.
2132:,
2078:if
2076:,
2032:,
1910:if
1908:,
1864:,
1812:→
1804:→
1351:.
1322:→
1302:→
1227:→
1219:→
1038:,
1012:,
952:,
843:,
817:,
791:,
762:OR
734:,
707:,
684:,
618:,
592:,
525:,
499:,
432:,
406:,
380:,
313:,
287:,
227:,
201:,
138:,
112:,
89:,
63:,
3381:/
3247:)
2990:/
2968:e
2961:t
2954:v
2914:.
2894:.
2861:.
2844:.
2804:.
2776:.
2668:P
2664:S
2650:)
2647:x
2644:(
2641:P
2635:)
2632:x
2629:(
2626:S
2623:.
2620:x
2580:A
2576:A
2572:A
2565:I
2557:E
2553:I
2549:E
2529:O
2513:I
2497:E
2479:A
2452:I
2448:E
2428:P
2420:S
2380:Q
2374:P
2354:Q
2348:P
2338:P
2334:Q
2330:Q
2326:P
2300:}
2297:R
2291:)
2288:b
2285:,
2282:a
2279:(
2276::
2273:)
2270:a
2267:,
2264:b
2261:(
2258:{
2255:=
2250:T
2246:R
2222:,
2219:B
2213:A
2207:R
2183:R
2145:c
2118:2
2114:c
2110:=
2105:2
2101:b
2097:+
2092:2
2088:a
2063:c
2041:b
2019:a
1991:.
1976:2
1972:c
1968:=
1963:2
1959:b
1955:+
1950:2
1946:a
1921:c
1895:c
1873:b
1851:a
1829:"
1825:"
1814:P
1810:Q
1806:Q
1802:P
1790:P
1786:Q
1700:Q
1655:P
1611:Q
1605:P
1581:Q
1558:P
1545:Q
1538:P
1534:S
1522:T
1519:T
1516:T
1513:T
1508:T
1505:F
1502:F
1499:T
1494:F
1491:T
1488:T
1485:F
1480:T
1477:T
1474:F
1471:F
1454:Q
1448:P
1427:Q
1421:P
1400:Q
1379:P
1364:S
1360:S
1342:Q
1335:P
1328:S
1324:P
1320:Q
1318:(
1312:S
1304:Q
1300:P
1298:(
1292:S
1271:Q
1265:P
1229:P
1225:Q
1221:Q
1217:P
1189:e
1182:t
1175:v
1052:B
1046:A
1026:B
1020:A
1000:B
994:A
966:B
960:A
940:B
927:A
899:B
885:A
857:B
851:A
831:B
825:A
805:B
802:+
799:A
779:B
773:A
745:A
717:A
695:A
672:A
635:B
632:+
629:A
606:B
600:A
580:B
567:A
539:B
533:A
513:B
507:A
487:B
481:A
449:B
443:A
420:B
414:A
394:B
388:A
368:B
355:A
327:B
321:A
301:B
295:A
275:B
269:A
241:B
235:A
215:B
209:A
189:B
183:A
155:B
146:A
126:B
120:A
100:B
97:A
77:B
71:A
51:B
45:A
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