A) \[(\tilde{\ }p\vee \tilde{\ }q)\equiv (p\wedge q)\]
B) \[(p\to q)\equiv (\tilde{\ }q\to \tilde{\ }p)\]
C) \[\tilde{\ }(p\to \tilde{\ }q)\equiv (p\wedge \tilde{\ }q)\]
D) \[\tilde{\ }(p\leftrightarrow q)\equiv (p\to q)\to (q\to p)\]
Correct Answer: B
Solution :
[b] Since \[\tilde{\ }(p\vee q)\equiv (\tilde{\ }p\wedge \tilde{\ }q)\] and \[\tilde{\ }(p\wedge q)\equiv (\tilde{\ }p\vee q)\] So option [b] and [d] are not true. \[(p\to q)\equiv p\wedge \tilde{\ }q),\]So option [c] is not true. Now \[p\to q\tilde{\ }p\vee q\] \[\tilde{\ }q\to \tilde{\ }p\equiv [\tilde{\ }(\tilde{\ }q)\vee \tilde{\ }p]\equiv q\vee \tilde{\ }p\equiv \tilde{\ }p\vee q\] \[p\to q\equiv \tilde{\ }q\to \tilde{\ }p\]
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