Mathematical Logic And Boolean Algebra Question 42
Question: The contrapositive of $ p\to (\tilde{\ }q\to \tilde{\ }r) $ is-
Options:
A) $ (\tilde{\ }q\wedge r)\to \tilde{\ }p $
B) $ (q\to r)\to \tilde{\ }p $
C) $ (q\vee \tilde{\ }r)\to \tilde{\ }p $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] We know that the contrapositive of $ p\to q $ is $ \tilde{\ }q\to \tilde{\ }p. $ so contra positive of $ p\to (\tilde{\ }q\to \tilde{\ }r) $ is $ \tilde{\ }(\tilde{\ }q\to \tilde{\ }r)\to \tilde{\ }p\equiv \tilde{\ }q\wedge [\tilde{\ }(\tilde{\ }r)]\tilde{\ }p $ $ \because \tilde{\ }(p\to q)\equiv p\wedge \tilde{\ }q\equiv \tilde{\ }q\wedge r\to \tilde{\ }p $
BETA
