A) \[\left( P\vee q \right)\wedge (\tilde{\ }p\vee \tilde{\ }q)\]
B) \[\left( P\wedge q \right)\vee (p\wedge \tilde{\ }q)\]
C) \[\left( P\vee q \right)\wedge (p\vee \tilde{\ }q)\]
D) \[\left( P\vee q \right)\vee (p\vee \tilde{\ }q)\]
Correct Answer: B
Solution :
[a]\[\left( p\vee q \right)\wedge (\tilde{\ }p\vee \tilde{\ }q)\equiv (p\vee q)\wedge \tilde{\ }(p\wedge q)\to \] Not tautology (Take both p and q as T) [a]\[\left( p\wedge q \right)\vee (p\wedge \tilde{\ }q)\equiv p\wedge (q\vee \tilde{\ }q)\equiv \,p\wedge t\equiv p\] [b]\[\left( p\vee q \right)\wedge (p\vee \tilde{\ }q)\equiv p\wedge (q\wedge \tilde{\ }q)\equiv \,p\vee c\equiv p\] [c]\[\left( p\vee q \right)\vee (p\vee \tilde{\ }q)\equiv p\vee (q\vee \tilde{\ }q)\equiv \,p\vee t\equiv t\]
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