Mathematical Logic And Boolean Algebra Question 18
Question: The following statement $ (p\to q)\to [(\tilde{\ }p\to q)\to q] $ is
Options:
A) a fallacy
B) a tautology
C) equivalent to $ \neg p\to q $
D) equivalent to $ p\to \neg q $
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Answer:
Correct Answer: D
Solution:
$ \tilde{\ }s\vee (\tilde{\ }r\wedge s)=(\tilde{\ }s\vee \tilde{\ }r)\wedge (\tilde{\ }s\vee s) $ $ =\tilde{\ }(\tilde{\ }s\wedge r)\wedge \tilde{\ }t $ $ =\tilde{\ }(s\wedge r) $ So, negation is $ s\wedge r $ .
BETA
