Examples
Dylan Jager-Kujawa edited this page May 1, 2017
·
1 revision
Contraposition:
(P->Q)->(!Q->!P)
https://www.jager-kujawa.com/Gentzen/?p=(P-%3EQ)-%3E(!Q-%3E!P)
Definition of Implication:
((P->Q)->(!P||Q))&&((!P||Q)->(P->Q))
https://www.jager-kujawa.com/Gentzen/?p=((P-%3EQ)-%3E(!P%7C%7CQ))%26%26((!P%7C%7CQ)-%3E(P-%3EQ))
Distributive Property:
((P&&(Q||R))->((P&&Q)||(P&&R)))
https://www.jager-kujawa.com/Gentzen/?p=((P%26%26(Q%7C%7CR))-%3E((P%26%26Q)%7C%7C(P%26%26R)))
((P||(Q&&R))->((P||Q)&&(P||R)))
https://www.jager-kujawa.com/Gentzen/?p=((P%7C%7C(Q%26%26R))-%3E((P%7C%7CQ)%26%26(P%7C%7CR)))
De Morgan:
(!(P&&Q)->(!P||!Q))&&((!P||!Q)->!(P&&Q))
(!(P||Q)->(!P&&!Q))&&((!P&&!Q)->!(P||Q))
Exportation:
((P&&Q)->R)->(P->(Q->R))
https://www.jager-kujawa.com/Gentzen/?p=((P%26%26Q)-%3ER)-%3E(P-%3E(Q-%3ER))
Hypothetical Syllogism:
((P->Q)&&(Q->R))->(P->R)
https://www.jager-kujawa.com/Gentzen/?p=((P-%3EQ)%26%26(Q-%3ER))-%3E(P-%3ER)
False:
((P&&Q)->R)->((P->R)&&(Q->R))
https://www.jager-kujawa.com/Gentzen/?p=((P%26%26Q)-%3ER)-%3E((P-%3ER)%26%26(Q-%3ER))