A) \[(p\ \wedge \tilde{\ }q)\ \wedge \tilde{\ }p\]
B) \[(p\ \wedge \tilde{\ }q)\ \vee \tilde{\ }p\]
C) \[(p\ \vee \tilde{\ }q)\ \vee \tilde{\ }p\]
D) None of these
Correct Answer: A
Solution :
\[\tilde{\ }[p\vee (\tilde{\ }p\vee q)]\equiv \,\tilde{\ }p\ \wedge \tilde{\ }(\tilde{\ }p\vee q)\] \[\equiv \ \tilde{\ }p\wedge (\tilde{\ }(\tilde{\ }p)\ \wedge \tilde{\ }q)\] \[\equiv \tilde{\ }p\wedge (p\ \wedge \tilde{\ }q)\].
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