3033:
1171:
1262:
1787:
1759:
1729:
3427:
2697:
2179:
1365:
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
2453:"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."
1191:
2321:
2593:
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
534:
2671:
961:
476:
389:
3218:
2243:
1834:
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
601:
262:
920:
560:
236:
2141:
1999:
662:
3247:
1752:
1654:
1358:
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
743:
1448:
508:
348:
296:
176:
3323:
2375:
1632:
1475:
1292:
1073:
1021:
627:
3348:
3123:
878:
3294:
3094:
415:
2401:
1047:
322:
3069:
987:
210:
147:
98:
72:
852:
800:
441:
3377:
1721:
1602:
766:
693:
3414:
3189:
3152:
3023:
1781:
1697:
826:
716:
121:
2605:, this switch from the universal to the particular causes problems with empty categories: "All unicorns are mammals" is often taken as true, while the converse
2204:
2166:
2084:
2062:
2040:
1942:
1916:
1894:
1872:
1676:
1579:
1421:
1400:
1198:
2566:
propositions can be expressed by the restriction that "No term must be distributed in the converse which is not distributed in the convertend." For
2977:
1184:
17:
1366:"If I am a three-sided polygon, then I am a triangle," because the definition of "triangle" is "three-sided polygon".
2970:
2673:. It is therefore clear that the categorical converse is closely related to the implicational converse, and that
2251:
1223:
of a categorical or implicational statement is the result of reversing its two constituent statements. For the
2799:
513:
2623:
2420:
933:
446:
361:
3455:
3450:
3203:
2963:
2213:
1174:
573:
241:
2457:
The "exposita" is more usually called the "convertend". In its simple form, conversion is valid only for
891:
539:
2774:
215:
2408:
2093:
1951:
632:
3232:
1827:. The converse may or may not be true, and even if true, the proof may be difficult. For example, the
1737:
1639:
1253:. Either way, the truth of the converse is generally independent from that of the original statement.
721:
1427:
487:
327:
275:
152:
3308:
2354:
1611:
1540:
1454:
1271:
1052:
1000:
606:
3333:
3108:
2585:
propositions, the subject is distributed while the predicate is not, and so the inference from an
2425:
In traditional logic, the process of switching the subject term with the predicate term is called
857:
3327:
3298:
3279:
3079:
2597:
to be the process of producing this weaker statement. Inference from a statement to its converse
1243:
1121:
394:
2380:
1026:
301:
3054:
1091:
966:
189:
2869:
126:
77:
51:
3222:
3168:
2902:
2852:
2740:
2571:
831:
779:
420:
182:
3362:
1703:
1584:
748:
675:
3399:
3174:
3137:
3098:
3008:
2008:
1766:
1682:
1224:
1149:
268:
8:
3352:
3127:
1843:
1828:
1159:
805:
772:
44:
698:
103:
2987:
2725:
2189:
2151:
2069:
2047:
2025:
1927:
1901:
1879:
1857:
1661:
1564:
1406:
1385:
1342:
1154:
33:
3431:
3251:
2998:
2702:
2613:
2246:
1096:
3032:
1116:
2178:
2881:
2825:
2720:
2207:
1101:
3255:
3044:
2945:
2833:
2715:
1111:
354:
3444:
3393:
3389:
3002:
2955:
1359:
1126:
3193:
1265:
926:
3302:
3269:
2928:
1216:
1106:
566:
3102:
2735:
1349:
1144:
3226:
3048:
2918:
2844:
2730:
2710:
2602:
2446:
884:
3356:
3273:
3197:
3164:
1561:
Converse implication is logically equivalent to the disjunction of
668:
1377:
are not logically equivalent, unless both terms imply each other:
3131:
2589:
statement to its converse is not valid. As an example, for the
1831:
was proved in 1912, but its converse was proved only in 1997.
1212:
2849:
The
Science of Logic: or, An Analysis of the Laws of Thought
1558:
is also true), then affirming the consequent will be valid.
1786:
1758:
1728:
1261:
1552:
1539:
Going from a statement to its converse is the fallacy of
1341:
says nothing about the truth of its converse, unless the
1811:
In mathematics, the converse of a theorem of the form
3402:
3365:
3336:
3311:
3282:
3235:
3206:
3177:
3140:
3111:
3082:
3057:
3011:
2775:"What Are the Converse, Contrapositive, and Inverse?"
2626:
2383:
2357:
2254:
2216:
2192:
2154:
2096:
2072:
2050:
2028:
1954:
1930:
1904:
1882:
1860:
1769:
1740:
1706:
1685:
1664:
1642:
1614:
1587:
1567:
1457:
1430:
1409:
1388:
1274:
1055:
1029:
1003:
969:
936:
894:
860:
834:
808:
782:
751:
724:
701:
678:
635:
609:
576:
542:
516:
490:
449:
423:
397:
364:
330:
304:
278:
244:
218:
192:
155:
129:
106:
80:
54:
2692:
27:
Reverse of a categorical or hypothetical proposition
2899:
The World and
Language in Wittgenstein's Philosophy
3408:
3371:
3342:
3317:
3288:
3241:
3212:
3183:
3146:
3117:
3088:
3063:
3017:
2864:William Thomas Parry and Edward A. Hacker (1991),
2763:, 2nd ed., Cambridge University Press: "converse".
2665:
2395:
2369:
2315:
2237:
2198:
2160:
2135:
2078:
2056:
2034:
1993:
1936:
1910:
1888:
1866:
1775:
1746:
1715:
1691:
1670:
1648:
1626:
1596:
1573:
1469:
1442:
1415:
1394:
1296:The white area shows where the statement is false.
1286:
1067:
1041:
1015:
981:
955:
914:
872:
846:
820:
794:
760:
737:
710:
687:
656:
621:
595:
554:
528:
502:
470:
435:
409:
383:
342:
316:
290:
256:
230:
204:
170:
141:
115:
92:
66:
1795:In natural language, this could be rendered "not
3442:
2985:
2609:"Some mammals are unicorns" is clearly false.
2971:
2570:propositions, both subject and predicate are
1192:
2310:
2268:
2014:(Book I, Proposition 48), can be stated as:
2558:The validity of simple conversion only for
2978:
2964:
2800:"The Four Vertex Theorem and its Converse"
2797:
2316:{\displaystyle R^{T}=\{(b,a):(a,b)\in R\}}
1199:
1185:
2421:Categorical proposition § Conversion
2173:
1256:
2177:
1806:
1260:
2414:
2182:Converse a simple mathematical relation
1547:and its converse are equivalent (i.e.,
529:{\displaystyle A\not \Leftrightarrow B}
14:
3443:
2761:The Cambridge Dictionary of Philosophy
2666:{\displaystyle \forall x.S(x)\to P(x)}
2147:the angle opposite the side of length
1923:the angle opposite the side of length
956:{\displaystyle A{\underline {\lor }}B}
471:{\displaystyle {\overline {A\cdot B}}}
384:{\displaystyle A{\overline {\land }}B}
3213:{\displaystyle \not \leftrightarrow }
2959:
2601:is generally valid. However, as with
2238:{\displaystyle R\subseteq A\times B,}
596:{\displaystyle A{\overline {\lor }}B}
257:{\displaystyle A\leftrightharpoons B}
2798:Shonkwiler, Clay (October 6, 2006).
2007:The converse, which also appears in
2753:
915:{\displaystyle A\ {\text{XNOR}}\ B}
555:{\displaystyle A\nleftrightarrow B}
24:
3403:
3178:
3012:
2942:. MacMillan, 1979, fifth edition.
2912:
2772:
2627:
1707:
1588:
1369:A truth table makes it clear that
679:
231:{\displaystyle A\Leftrightarrow B}
162:
159:
133:
25:
3467:
2136:{\displaystyle a^{2}+b^{2}=c^{2}}
1994:{\displaystyle a^{2}+b^{2}=c^{2}}
657:{\displaystyle {\overline {A+B}}}
3425:
3242:{\displaystyle \leftrightarrow }
3031:
2695:
2335:The converse of the implication
2021:a triangle with sides of length
1853:a triangle with sides of length
1785:
1757:
1747:{\displaystyle \Leftrightarrow }
1727:
1649:{\displaystyle \Leftrightarrow }
1170:
1169:
738:{\displaystyle {\overline {A}}}
3283:
3236:
3112:
3083:
3058:
2950:A Modern Introduction to Logic
2891:
2875:
2858:
2838:
2828:& Thomas Ströhlein (1993)
2819:
2791:
2766:
2660:
2654:
2648:
2645:
2639:
2614:first-order predicate calculus
2429:. For example, going from "No
2361:
2301:
2289:
2283:
2271:
1741:
1643:
1618:
1461:
1443:{\displaystyle P\rightarrow Q}
1434:
1278:
1059:
1007:
613:
503:{\displaystyle A\not \equiv B}
401:
343:{\displaystyle A\rightarrow B}
334:
291:{\displaystyle A\Rightarrow B}
282:
248:
222:
171:{\displaystyle A\&\&B}
13:
1:
3318:{\displaystyle \nrightarrow }
2888:, C. Scribner's sons, p. 156.
2746:
2370:{\displaystyle P\leftarrow Q}
1838:will be "Given P, if R then Q
1627:{\displaystyle P\leftarrow Q}
1470:{\displaystyle P\leftarrow Q}
1287:{\displaystyle P\leftarrow Q}
1068:{\displaystyle A\leftarrow B}
1016:{\displaystyle A\Leftarrow B}
622:{\displaystyle A\downarrow B}
3343:{\displaystyle \nleftarrow }
3118:{\displaystyle \rightarrow }
1543:. However, if the statement
1337:). In general, the truth of
873:{\displaystyle A\parallel B}
730:
649:
585:
463:
373:
7:
3289:{\displaystyle \downarrow }
3089:{\displaystyle \leftarrow }
2688:
2330:
1305:be a statement of the form
410:{\displaystyle A\uparrow B}
10:
3472:
2578:propositions, neither is.
2418:
2396:{\displaystyle P\subset Q}
2377:, but may also be notated
1355:are logically equivalent.
1042:{\displaystyle A\subset B}
317:{\displaystyle A\supset B}
3422:
3385:
3265:
3160:
3064:{\displaystyle \uparrow }
3040:
3029:
2994:
2952:. Cromwell Company, 1931.
2759:Robert Audi, ed. (1999),
982:{\displaystyle A\oplus B}
205:{\displaystyle A\equiv B}
2897:Gordon Hunnings (1988),
1541:affirming the consequent
142:{\displaystyle A\&B}
93:{\displaystyle A\cdot B}
67:{\displaystyle A\land B}
3328:Converse nonimplication
1244:categorical proposition
1122:Functional completeness
847:{\displaystyle A\mid B}
795:{\displaystyle A\lor B}
436:{\displaystyle A\mid B}
3410:
3373:
3372:{\displaystyle \land }
3344:
3319:
3290:
3243:
3214:
3185:
3148:
3119:
3090:
3065:
3019:
2667:
2620:can be represented as
2455:
2397:
2371:
2317:
2239:
2200:
2183:
2174:Converse of a relation
2171:
2162:
2137:
2080:
2058:
2036:
2005:
1995:
1938:
1912:
1890:
1868:
1777:
1748:
1717:
1716:{\displaystyle \neg Q}
1693:
1672:
1650:
1628:
1598:
1597:{\displaystyle \neg Q}
1575:
1471:
1444:
1417:
1396:
1298:
1288:
1257:Implicational converse
1092:Propositional calculus
1069:
1043:
1017:
983:
957:
916:
874:
848:
822:
796:
762:
761:{\displaystyle \sim A}
739:
712:
689:
688:{\displaystyle \neg A}
658:
623:
597:
556:
530:
504:
472:
437:
411:
385:
344:
318:
292:
258:
232:
206:
172:
143:
117:
94:
68:
3432:Philosophy portal
3411:
3409:{\displaystyle \bot }
3374:
3345:
3320:
3291:
3244:
3215:
3186:
3184:{\displaystyle \neg }
3149:
3147:{\displaystyle \lor }
3120:
3091:
3066:
3020:
3018:{\displaystyle \top }
2933:Introduction to Logic
2886:The Elements of Logic
2741:Transposition (logic)
2681:cannot be swapped in
2668:
2451:
2398:
2372:
2318:
2240:
2201:
2181:
2163:
2138:
2081:
2059:
2037:
2016:
1996:
1939:
1913:
1891:
1869:
1848:
1807:Converse of a theorem
1778:
1776:{\displaystyle \lor }
1749:
1718:
1694:
1692:{\displaystyle \lor }
1673:
1651:
1629:
1599:
1576:
1472:
1445:
1418:
1397:
1289:
1264:
1150:Programming languages
1070:
1044:
1018:
984:
958:
917:
875:
849:
823:
797:
763:
740:
713:
690:
659:
624:
598:
557:
531:
505:
473:
438:
412:
386:
345:
319:
293:
259:
233:
207:
173:
144:
118:
95:
69:
3400:
3363:
3334:
3309:
3280:
3233:
3204:
3175:
3138:
3109:
3080:
3074:Converse implication
3055:
3009:
2830:Relations and Graphs
2624:
2484:(valid if P exists)
2437:to its converse "No
2415:Categorical converse
2381:
2355:
2252:
2214:
2190:
2152:
2094:
2070:
2048:
2026:
1952:
1928:
1902:
1880:
1858:
1767:
1738:
1704:
1683:
1662:
1640:
1612:
1585:
1565:
1455:
1428:
1407:
1386:
1373:and the converse of
1272:
1053:
1027:
1001:
967:
934:
892:
858:
832:
806:
780:
749:
722:
699:
676:
633:
607:
574:
540:
514:
488:
447:
421:
395:
362:
328:
302:
276:
242:
216:
190:
153:
127:
104:
78:
52:
3456:Immediate inference
3451:Logical connectives
2988:logical connectives
2935:. MacMillan, 1953.
2323:is also called the
1844:Pythagorean theorem
1842:. For example, the
1829:four-vertex theorem
1160:Philosophy of logic
821:{\displaystyle A+B}
34:Logical connectives
3406:
3369:
3340:
3315:
3286:
3239:
3210:
3181:
3144:
3115:
3086:
3061:
3045:Alternative denial
3015:
2866:Aristotelian Logic
2807:math.colostate.edu
2773:Taylor, Courtney.
2726:Logical connective
2663:
2445:. In the words of
2409:Bocheński notation
2393:
2367:
2313:
2235:
2196:
2184:
2169:is a right angle.
2158:
2133:
2076:
2054:
2032:
1991:
1945:is a right angle,
1934:
1908:
1886:
1864:
1846:can be stated as:
1773:
1744:
1713:
1689:
1668:
1646:
1624:
1594:
1571:
1467:
1440:
1413:
1392:
1299:
1284:
1249:, the converse is
1234:, the converse is
1155:Mathematical logic
1065:
1039:
1013:
979:
953:
948:
912:
870:
844:
818:
792:
758:
735:
711:{\displaystyle -A}
708:
685:
654:
619:
593:
552:
526:
500:
468:
433:
407:
381:
340:
314:
288:
254:
228:
202:
168:
139:
116:{\displaystyle AB}
113:
90:
64:
18:Conversion (logic)
3438:
3437:
2703:Philosophy portal
2556:
2555:
2247:converse relation
2199:{\displaystyle R}
2161:{\displaystyle c}
2079:{\displaystyle c}
2057:{\displaystyle b}
2035:{\displaystyle a}
1937:{\displaystyle c}
1911:{\displaystyle c}
1889:{\displaystyle b}
1867:{\displaystyle a}
1793:
1792:
1671:{\displaystyle P}
1574:{\displaystyle P}
1537:
1536:
1416:{\displaystyle Q}
1395:{\displaystyle P}
1325:is the statement
1297:
1209:
1208:
1078:
1077:
941:
908:
904:
900:
733:
652:
588:
466:
376:
16:(Redirected from
3463:
3430:
3429:
3428:
3415:
3413:
3412:
3407:
3378:
3376:
3375:
3370:
3349:
3347:
3346:
3341:
3324:
3322:
3321:
3316:
3295:
3293:
3292:
3287:
3248:
3246:
3245:
3240:
3219:
3217:
3216:
3211:
3190:
3188:
3187:
3182:
3153:
3151:
3150:
3145:
3124:
3122:
3121:
3116:
3095:
3093:
3092:
3087:
3070:
3068:
3067:
3062:
3035:
3024:
3022:
3021:
3016:
2980:
2973:
2966:
2957:
2956:
2906:
2895:
2889:
2879:
2873:
2862:
2856:
2842:
2836:
2823:
2817:
2816:
2814:
2813:
2804:
2795:
2789:
2788:
2786:
2785:
2770:
2764:
2757:
2705:
2700:
2699:
2698:
2672:
2670:
2669:
2664:
2518:Some P is not S
2468:
2467:
2402:
2400:
2399:
2394:
2376:
2374:
2373:
2368:
2322:
2320:
2319:
2314:
2264:
2263:
2244:
2242:
2241:
2236:
2205:
2203:
2202:
2197:
2167:
2165:
2164:
2159:
2142:
2140:
2139:
2134:
2132:
2131:
2119:
2118:
2106:
2105:
2085:
2083:
2082:
2077:
2063:
2061:
2060:
2055:
2041:
2039:
2038:
2033:
2000:
1998:
1997:
1992:
1990:
1989:
1977:
1976:
1964:
1963:
1943:
1941:
1940:
1935:
1917:
1915:
1914:
1909:
1895:
1893:
1892:
1887:
1873:
1871:
1870:
1865:
1789:
1782:
1780:
1779:
1774:
1761:
1753:
1751:
1750:
1745:
1731:
1722:
1720:
1719:
1714:
1698:
1696:
1695:
1690:
1677:
1675:
1674:
1669:
1655:
1653:
1652:
1647:
1633:
1631:
1630:
1625:
1606:
1605:
1603:
1601:
1600:
1595:
1580:
1578:
1577:
1572:
1476:
1474:
1473:
1468:
1449:
1447:
1446:
1441:
1422:
1420:
1419:
1414:
1401:
1399:
1398:
1393:
1380:
1379:
1295:
1293:
1291:
1290:
1285:
1201:
1194:
1187:
1173:
1172:
1117:Boolean function
1083:Related concepts
1074:
1072:
1071:
1066:
1048:
1046:
1045:
1040:
1022:
1020:
1019:
1014:
988:
986:
985:
980:
962:
960:
959:
954:
949:
921:
919:
918:
913:
906:
905:
902:
898:
879:
877:
876:
871:
853:
851:
850:
845:
827:
825:
824:
819:
801:
799:
798:
793:
767:
765:
764:
759:
744:
742:
741:
736:
734:
726:
717:
715:
714:
709:
694:
692:
691:
686:
663:
661:
660:
655:
653:
648:
637:
628:
626:
625:
620:
602:
600:
599:
594:
589:
581:
561:
559:
558:
553:
535:
533:
532:
527:
509:
507:
506:
501:
477:
475:
474:
469:
467:
462:
451:
442:
440:
439:
434:
416:
414:
413:
408:
390:
388:
387:
382:
377:
369:
349:
347:
346:
341:
323:
321:
320:
315:
297:
295:
294:
289:
263:
261:
260:
255:
237:
235:
234:
229:
211:
209:
208:
203:
177:
175:
174:
169:
148:
146:
145:
140:
122:
120:
119:
114:
99:
97:
96:
91:
73:
71:
70:
65:
41:
40:
30:
29:
21:
3471:
3470:
3466:
3465:
3464:
3462:
3461:
3460:
3441:
3440:
3439:
3434:
3426:
3424:
3418:
3401:
3398:
3397:
3381:
3364:
3361:
3360:
3335:
3332:
3331:
3310:
3307:
3306:
3281:
3278:
3277:
3261:
3234:
3231:
3230:
3205:
3202:
3201:
3176:
3173:
3172:
3156:
3139:
3136:
3135:
3110:
3107:
3106:
3081:
3078:
3077:
3056:
3053:
3052:
3036:
3027:
3010:
3007:
3006:
2990:
2984:
2946:Stebbing, Susan
2915:
2913:Further reading
2910:
2909:
2896:
2892:
2882:James H. Hyslop
2880:
2876:
2863:
2859:
2843:
2839:
2826:Gunther Schmidt
2824:
2820:
2811:
2809:
2802:
2796:
2792:
2783:
2781:
2771:
2767:
2758:
2754:
2749:
2721:Inverse (logic)
2701:
2696:
2694:
2691:
2625:
2622:
2621:
2544:Some S is not P
2477:Simple converse
2423:
2417:
2382:
2379:
2378:
2356:
2353:
2352:
2343:may be written
2333:
2259:
2255:
2253:
2250:
2249:
2215:
2212:
2211:
2208:binary relation
2191:
2188:
2187:
2176:
2153:
2150:
2149:
2127:
2123:
2114:
2110:
2101:
2097:
2095:
2092:
2091:
2071:
2068:
2067:
2049:
2046:
2045:
2027:
2024:
2023:
1985:
1981:
1972:
1968:
1959:
1955:
1953:
1950:
1949:
1929:
1926:
1925:
1903:
1900:
1899:
1881:
1878:
1877:
1859:
1856:
1855:
1809:
1768:
1765:
1764:
1754:
1739:
1736:
1735:
1705:
1702:
1701:
1684:
1681:
1680:
1663:
1660:
1659:
1656:
1641:
1638:
1637:
1613:
1610:
1609:
1586:
1583:
1582:
1566:
1563:
1562:
1456:
1453:
1452:
1429:
1426:
1425:
1408:
1405:
1404:
1387:
1384:
1383:
1294:
1273:
1270:
1269:
1259:
1205:
1164:
1131:
1102:Boolean algebra
1097:Predicate logic
1054:
1051:
1050:
1028:
1025:
1024:
1002:
999:
998:
968:
965:
964:
940:
935:
932:
931:
901:
893:
890:
889:
859:
856:
855:
833:
830:
829:
807:
804:
803:
781:
778:
777:
750:
747:
746:
725:
723:
720:
719:
700:
697:
696:
677:
674:
673:
638:
636:
634:
631:
630:
608:
605:
604:
580:
575:
572:
571:
541:
538:
537:
515:
512:
511:
489:
486:
485:
452:
450:
448:
445:
444:
422:
419:
418:
396:
393:
392:
368:
363:
360:
359:
329:
326:
325:
303:
300:
299:
277:
274:
273:
243:
240:
239:
217:
214:
213:
191:
188:
187:
154:
151:
150:
128:
125:
124:
105:
102:
101:
79:
76:
75:
53:
50:
49:
28:
23:
22:
15:
12:
11:
5:
3469:
3459:
3458:
3453:
3436:
3435:
3423:
3420:
3419:
3417:
3416:
3405:
3386:
3383:
3382:
3380:
3379:
3368:
3350:
3339:
3325:
3314:
3299:Nonimplication
3296:
3285:
3266:
3263:
3262:
3260:
3259:
3256:Digital buffer
3249:
3238:
3220:
3209:
3191:
3180:
3161:
3158:
3157:
3155:
3154:
3143:
3125:
3114:
3096:
3085:
3071:
3060:
3041:
3038:
3037:
3030:
3028:
3026:
3025:
3014:
2995:
2992:
2991:
2983:
2982:
2975:
2968:
2960:
2954:
2953:
2943:
2940:Symbolic Logic
2938:Copi, Irving.
2936:
2926:
2914:
2911:
2908:
2907:
2901:, SUNY Press,
2890:
2874:
2868:, SUNY Press,
2857:
2837:
2834:Springer books
2818:
2790:
2765:
2751:
2750:
2748:
2745:
2744:
2743:
2738:
2733:
2728:
2723:
2718:
2716:Contraposition
2713:
2707:
2706:
2690:
2687:
2662:
2659:
2656:
2653:
2650:
2647:
2644:
2641:
2638:
2635:
2632:
2629:
2554:
2553:
2550:
2545:
2542:
2536:
2535:
2532:
2529:
2526:
2520:
2519:
2516:
2513:
2510:
2504:
2503:
2500:
2495:
2492:
2486:
2485:
2478:
2475:
2472:
2465:propositions:
2416:
2413:
2392:
2389:
2386:
2366:
2363:
2360:
2332:
2329:
2312:
2309:
2306:
2303:
2300:
2297:
2294:
2291:
2288:
2285:
2282:
2279:
2276:
2273:
2270:
2267:
2262:
2258:
2234:
2231:
2228:
2225:
2222:
2219:
2195:
2175:
2172:
2157:
2130:
2126:
2122:
2117:
2113:
2109:
2104:
2100:
2075:
2053:
2031:
1988:
1984:
1980:
1975:
1971:
1967:
1962:
1958:
1933:
1907:
1885:
1863:
1808:
1805:
1791:
1790:
1783:
1772:
1762:
1755:
1743:
1734:
1732:
1724:
1723:
1712:
1709:
1699:
1688:
1678:
1667:
1657:
1645:
1636:
1634:
1623:
1620:
1617:
1593:
1590:
1570:
1553:if and only if
1535:
1534:
1531:
1528:
1525:
1521:
1520:
1517:
1514:
1511:
1507:
1506:
1503:
1500:
1497:
1493:
1492:
1489:
1486:
1483:
1479:
1478:
1466:
1463:
1460:
1450:
1439:
1436:
1433:
1423:
1412:
1402:
1391:
1283:
1280:
1277:
1258:
1255:
1207:
1206:
1204:
1203:
1196:
1189:
1181:
1178:
1177:
1166:
1165:
1163:
1162:
1157:
1152:
1147:
1141:
1138:
1137:
1133:
1132:
1130:
1129:
1124:
1119:
1114:
1112:Truth function
1109:
1104:
1099:
1094:
1088:
1085:
1084:
1080:
1079:
1076:
1075:
1064:
1061:
1058:
1038:
1035:
1032:
1012:
1009:
1006:
996:
990:
989:
978:
975:
972:
952:
947:
944:
939:
929:
923:
922:
911:
897:
887:
881:
880:
869:
866:
863:
843:
840:
837:
817:
814:
811:
791:
788:
785:
775:
769:
768:
757:
754:
732:
729:
707:
704:
684:
681:
671:
665:
664:
651:
647:
644:
641:
618:
615:
612:
592:
587:
584:
579:
569:
563:
562:
551:
548:
545:
525:
522:
519:
499:
496:
493:
483:
479:
478:
465:
461:
458:
455:
432:
429:
426:
406:
403:
400:
380:
375:
372:
367:
357:
351:
350:
339:
336:
333:
313:
310:
307:
287:
284:
281:
271:
265:
264:
253:
250:
247:
227:
224:
221:
201:
198:
195:
185:
179:
178:
167:
164:
161:
158:
138:
135:
132:
112:
109:
89:
86:
83:
63:
60:
57:
47:
37:
36:
26:
9:
6:
4:
3:
2:
3468:
3457:
3454:
3452:
3449:
3448:
3446:
3433:
3421:
3395:
3391:
3390:Contradiction
3388:
3387:
3384:
3366:
3358:
3354:
3351:
3337:
3329:
3326:
3312:
3304:
3300:
3297:
3275:
3271:
3268:
3267:
3264:
3257:
3253:
3250:
3228:
3224:
3223:Biconditional
3221:
3207:
3199:
3195:
3192:
3170:
3166:
3163:
3162:
3159:
3141:
3133:
3129:
3126:
3104:
3100:
3097:
3075:
3072:
3050:
3046:
3043:
3042:
3039:
3034:
3004:
3000:
2997:
2996:
2993:
2989:
2981:
2976:
2974:
2969:
2967:
2962:
2961:
2958:
2951:
2947:
2944:
2941:
2937:
2934:
2930:
2927:
2924:
2920:
2917:
2916:
2904:
2900:
2894:
2887:
2883:
2878:
2871:
2867:
2861:
2854:
2850:
2846:
2841:
2835:
2831:
2827:
2822:
2808:
2801:
2794:
2780:
2776:
2769:
2762:
2756:
2752:
2742:
2739:
2737:
2734:
2732:
2729:
2727:
2724:
2722:
2719:
2717:
2714:
2712:
2709:
2708:
2704:
2693:
2686:
2684:
2680:
2676:
2657:
2651:
2642:
2636:
2633:
2630:
2619:
2615:
2610:
2608:
2604:
2600:
2596:
2592:
2588:
2584:
2579:
2577:
2573:
2569:
2565:
2561:
2551:
2549:
2546:
2543:
2541:
2538:
2537:
2533:
2530:
2527:
2525:
2522:
2521:
2517:
2514:
2511:
2509:
2506:
2505:
2501:
2499:
2496:
2493:
2491:
2488:
2487:
2483:
2479:
2476:
2473:
2470:
2469:
2466:
2464:
2460:
2454:
2450:
2448:
2444:
2440:
2436:
2432:
2428:
2422:
2412:
2410:
2406:
2390:
2387:
2384:
2364:
2358:
2350:
2346:
2342:
2338:
2328:
2326:
2307:
2304:
2298:
2295:
2292:
2286:
2280:
2277:
2274:
2265:
2260:
2256:
2248:
2232:
2229:
2226:
2223:
2220:
2217:
2209:
2193:
2180:
2170:
2168:
2155:
2146:
2128:
2124:
2120:
2115:
2111:
2107:
2102:
2098:
2090:
2086:
2073:
2064:
2051:
2042:
2029:
2020:
2015:
2013:
2012:
2004:
2003:
1986:
1982:
1978:
1973:
1969:
1965:
1960:
1956:
1948:
1944:
1931:
1922:
1918:
1905:
1896:
1883:
1874:
1861:
1852:
1847:
1845:
1841:
1837:
1832:
1830:
1826:
1822:
1818:
1814:
1804:
1802:
1798:
1788:
1784:
1770:
1763:
1760:
1756:
1733:
1730:
1726:
1725:
1710:
1700:
1686:
1679:
1665:
1658:
1635:
1621:
1615:
1608:
1607:
1604:
1591:
1568:
1559:
1557:
1554:
1550:
1546:
1542:
1532:
1529:
1526:
1523:
1522:
1518:
1515:
1512:
1509:
1508:
1504:
1501:
1498:
1495:
1494:
1490:
1487:
1484:
1481:
1480:
1464:
1458:
1451:
1437:
1431:
1424:
1410:
1403:
1389:
1382:
1381:
1378:
1376:
1372:
1367:
1363:
1361:
1356:
1354:
1351:
1347:
1344:
1340:
1336:
1332:
1328:
1324:
1320:
1316:
1312:
1308:
1304:
1281:
1275:
1267:
1263:
1254:
1252:
1248:
1245:
1241:
1237:
1233:
1229:
1226:
1222:
1218:
1214:
1202:
1197:
1195:
1190:
1188:
1183:
1182:
1180:
1179:
1176:
1168:
1167:
1161:
1158:
1156:
1153:
1151:
1148:
1146:
1145:Digital logic
1143:
1142:
1140:
1139:
1135:
1134:
1128:
1127:Scope (logic)
1125:
1123:
1120:
1118:
1115:
1113:
1110:
1108:
1105:
1103:
1100:
1098:
1095:
1093:
1090:
1089:
1087:
1086:
1082:
1081:
1062:
1056:
1036:
1033:
1030:
1010:
1004:
997:
995:
992:
991:
976:
973:
970:
950:
945:
942:
937:
930:
928:
925:
924:
909:
895:
888:
886:
883:
882:
867:
864:
861:
841:
838:
835:
815:
812:
809:
789:
786:
783:
776:
774:
771:
770:
755:
752:
727:
705:
702:
682:
672:
670:
667:
666:
645:
642:
639:
616:
610:
590:
582:
577:
570:
568:
565:
564:
549:
546:
543:
523:
520:
517:
497:
494:
491:
484:
482:nonequivalent
481:
480:
459:
456:
453:
430:
427:
424:
404:
398:
378:
370:
365:
358:
356:
353:
352:
337:
331:
311:
308:
305:
285:
279:
272:
270:
267:
266:
251:
245:
225:
219:
199:
196:
193:
186:
184:
181:
180:
165:
156:
136:
130:
110:
107:
87:
84:
81:
61:
58:
55:
48:
46:
43:
42:
39:
38:
35:
32:
31:
19:
3270:Joint denial
3194:Exclusive or
3073:
2949:
2939:
2932:
2929:Copi, Irving
2922:
2898:
2893:
2885:
2877:
2865:
2860:
2848:
2840:
2829:
2821:
2810:. Retrieved
2806:
2793:
2782:. Retrieved
2778:
2768:
2760:
2755:
2682:
2678:
2674:
2617:
2611:
2607:per accidens
2606:
2599:per accidens
2598:
2595:per accidens
2594:
2590:
2586:
2582:
2580:
2575:
2574:, while for
2567:
2563:
2559:
2557:
2547:
2539:
2523:
2507:
2502:Some P is S
2497:
2489:
2482:per accidens
2481:
2462:
2458:
2456:
2452:
2442:
2438:
2434:
2430:
2426:
2424:
2404:
2348:
2344:
2340:
2336:
2334:
2324:
2185:
2148:
2144:
2088:
2066:
2044:
2022:
2018:
2017:
2010:
2006:
2001:
1946:
1924:
1920:
1898:
1876:
1854:
1850:
1849:
1839:
1835:
1833:
1824:
1820:
1816:
1812:
1810:
1800:
1796:
1794:
1560:
1555:
1548:
1544:
1538:
1374:
1370:
1368:
1364:
1357:
1352:
1345:
1338:
1334:
1330:
1326:
1322:
1318:
1317:). Then the
1314:
1310:
1306:
1302:
1300:
1266:Venn diagram
1250:
1246:
1239:
1235:
1231:
1227:
1220:
1210:
1136:Applications
993:
3353:Conjunction
3303:NIMPLY gate
3128:Disjunction
3099:Implication
2683:All S are P
2618:All S are P
2572:distributed
2531:Some P is S
2528:Some S is P
2494:All S are P
1327:Q implies P
1307:P implies Q
1251:All P are S
1247:All S are P
1225:implication
1217:mathematics
1107:Truth table
3445:Categories
3103:IMPLY gate
2832:, page 9,
2812:2019-11-26
2784:2019-11-27
2747:References
2736:Term logic
2603:syllogisms
2474:Convertend
2427:conversion
2419:See also:
1477:(converse)
1350:consequent
1343:antecedent
1242:. For the
183:equivalent
3404:⊥
3367:∧
3338:↚
3313:↛
3284:↓
3252:Statement
3237:↔
3227:XNOR gate
3179:¬
3142:∨
3113:→
3084:←
3059:↑
3049:NAND gate
3013:⊤
2999:Tautology
2919:Aristotle
2845:Asa Mahan
2779:ThoughtCo
2731:Obversion
2711:Aristotle
2649:→
2628:∀
2548:not valid
2515:No P is S
2512:No S is P
2498:not valid
2480:Converse
2447:Asa Mahan
2388:⊂
2362:←
2325:transpose
2305:∈
2245:then the
2227:×
2221:⊆
2009:Euclid's
1771:∨
1742:⇔
1708:¬
1687:∨
1644:⇔
1619:←
1589:¬
1462:←
1435:→
1279:←
1060:←
1034:⊂
1008:⇐
974:⊕
946:_
943:∨
865:∥
839:∣
787:∨
753:∼
731:¯
703:−
680:¬
650:¯
614:↓
586:¯
583:∨
547:↮
464:¯
457:⋅
428:∣
402:↑
374:¯
371:∧
335:→
309:⊃
283:⇒
249:⇋
223:⇔
197:≡
163:&
160:&
134:&
85:⋅
59:∧
3357:AND gate
3274:NOR gate
3208:↮
3198:XOR gate
3169:NOT gate
3165:Negation
2884:(1892),
2689:See also
2331:Notation
2011:Elements
1819:will be
1799:without
1551:is true
1348:and the
1319:converse
1221:converse
1175:Category
994:converse
521:⇎
495:≢
3359:)
3355: (
3305:)
3301: (
3276:)
3272: (
3254: (
3229:)
3225: (
3200:)
3196: (
3171:)
3167: (
3134:)
3132:OR gate
3130: (
3105:)
3101: (
3051:)
3047: (
2986:Common
2923:Organon
2847:(1857)
2403:, or "B
269:implies
3396:
3330:
3076:
3005:
2870:p. 207
2407:" (in
2065:, and
1897:, and
1219:, the
907:
899:
3394:False
2903:p. 42
2853:p. 82
2803:(PDF)
2210:with
2206:is a
2019:Given
1851:Given
1213:logic
3003:True
2677:and
2581:For
2562:and
2471:Type
2461:and
2441:are
2433:are
2145:then
1947:then
1581:and
1360:true
1301:Let
1215:and
903:XNOR
885:XNOR
355:NAND
2612:In
2411:).
2186:If
1803:".
1321:of
1268:of
1211:In
927:XOR
669:NOT
567:NOR
45:AND
3447::
2948:.
2931:.
2921:.
2851:,
2805:.
2777:.
2685:.
2616:,
2552:–
2534:–
2449::
2443:S"
2435:P"
2405:pq
2351:,
2347:→
2339:→
2327:.
2143:,
2089:if
2087:,
2043:,
1921:if
1919:,
1875:,
1823:→
1815:→
1362:.
1333:→
1313:→
1238:→
1230:→
1049:,
1023:,
963:,
854:,
828:,
802:,
773:OR
745:,
718:,
695:,
629:,
603:,
536:,
510:,
443:,
417:,
391:,
324:,
298:,
238:,
212:,
149:,
123:,
100:,
74:,
3392:/
3258:)
3001:/
2979:e
2972:t
2965:v
2925:.
2905:.
2872:.
2855:.
2815:.
2787:.
2679:P
2675:S
2661:)
2658:x
2655:(
2652:P
2646:)
2643:x
2640:(
2637:S
2634:.
2631:x
2591:A
2587:A
2583:A
2576:I
2568:E
2564:I
2560:E
2540:O
2524:I
2508:E
2490:A
2463:I
2459:E
2439:P
2431:S
2391:Q
2385:P
2365:Q
2359:P
2349:P
2345:Q
2341:Q
2337:P
2311:}
2308:R
2302:)
2299:b
2296:,
2293:a
2290:(
2287::
2284:)
2281:a
2278:,
2275:b
2272:(
2269:{
2266:=
2261:T
2257:R
2233:,
2230:B
2224:A
2218:R
2194:R
2156:c
2129:2
2125:c
2121:=
2116:2
2112:b
2108:+
2103:2
2099:a
2074:c
2052:b
2030:a
2002:.
1987:2
1983:c
1979:=
1974:2
1970:b
1966:+
1961:2
1957:a
1932:c
1906:c
1884:b
1862:a
1840:"
1836:"
1825:P
1821:Q
1817:Q
1813:P
1801:P
1797:Q
1711:Q
1666:P
1622:Q
1616:P
1592:Q
1569:P
1556:Q
1549:P
1545:S
1533:T
1530:T
1527:T
1524:T
1519:T
1516:F
1513:F
1510:T
1505:F
1502:T
1499:T
1496:F
1491:T
1488:T
1485:F
1482:F
1465:Q
1459:P
1438:Q
1432:P
1411:Q
1390:P
1375:S
1371:S
1353:Q
1346:P
1339:S
1335:P
1331:Q
1329:(
1323:S
1315:Q
1311:P
1309:(
1303:S
1282:Q
1276:P
1240:P
1236:Q
1232:Q
1228:P
1200:e
1193:t
1186:v
1063:B
1057:A
1037:B
1031:A
1011:B
1005:A
977:B
971:A
951:B
938:A
910:B
896:A
868:B
862:A
842:B
836:A
816:B
813:+
810:A
790:B
784:A
756:A
728:A
706:A
683:A
646:B
643:+
640:A
617:B
611:A
591:B
578:A
550:B
544:A
524:B
518:A
498:B
492:A
460:B
454:A
431:B
425:A
405:B
399:A
379:B
366:A
338:B
332:A
312:B
306:A
286:B
280:A
252:B
246:A
226:B
220:A
200:B
194:A
166:B
157:A
137:B
131:A
111:B
108:A
88:B
82:A
62:B
56:A
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.