question_answer

The negation of \[p\to (\tilde{\ }p\vee q)\]is

A) \[p\vee (p\vee \tilde{\ }q)\]      

B) \[p\to \tilde{\ }(p\vee q)\]

C) \[p\to q\]                           

D) \[p\wedge \tilde{\ }q\]

Correct Answer: D

Solution :

Truth table Here, we observe that the truth value of column \[\sim [p\to (\sim p\vee q)]\]and \[(p\wedge \tilde{\ }q)\]are same. Hence,                  \[\tilde{\ }[p\to (\tilde{\ }p\vee q)]\equiv (p\wedge \tilde{\ }q)\]