Conditional Statements
pTTFFqTFTFp→qTFTT
p(전건)이 T(참)일때 vacuous truth(공허한 참) 문제가 발생한다.
ex1. ¬p∨q→¬qpTTFFqTFTF¬pFFTT¬p∨qTFTT¬qFTFT¬p∨q→¬qFTFT
ex2. p∨¬q→¬ppTTFFqTFTF¬qFTFTp∨¬qTTFT¬pFFTTp∨¬q→¬pFFTT
ex3. ¬p∨q≡p→qpTTFFqTFTF¬pFFTT¬p∨qTFTTp→qTFTT
Negation of Conditional Statements
p→q≡¬p∨q¬(p→q)≡¬(¬p)∧¬q≡p∧¬qso,¬(p→q)≡p∧¬q
contrapositive
contrapositive of p→q is ¬q→¬pp→q≡¬q→¬p
proof p→q≡¬q→¬ppTTFFqTFTFp→qTFTT¬qFTFT¬pFFTT¬q→¬pTFTT