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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