A) \[\tilde{\ }\left( p\wedge \tilde{\ }q \right)\to p\vee q\]
B) \[p\vee (~\sim q)\to p\wedge q\]
C) \[\sim \left( p\vee \tilde{\ }q \right)\to p\vee q\]
D) \[~\sim (p\vee \sim ~q)\to p\wedge q\]
Correct Answer: C
Solution :
\[\because \,\,\,\,\,\,\,p\to q=q\vee \tilde{\ }P\] \[\therefore \] Checking option \[3\tilde{\ }\left( p\vee -q \right)\to \left( p\vee q \right)\] is equivalent to \[\Rightarrow \,\,\,\,\,\,\left( p\vee q \right)\vee \left( p\vee \tilde{\ }q \right)\] \[\Rightarrow \,\,\,\,\,\,p\vee T\equiv T\]
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