A) \[(p\vee \tilde{\ }q)\wedge (q\wedge \tilde{\ }p)\]
B) \[(p\wedge \tilde{\ }q)\vee (q\wedge \tilde{\ }p)\]
C) \[(p\wedge \tilde{\ }q)\wedge (q\wedge \tilde{\ }p)\]
D) None of the above
Correct Answer: B
Solution :
\[\tilde{\ }(p\Leftrightarrow q)=\tilde{\ }[(p\Rightarrow q)\wedge (q\Rightarrow p)]\] \[=-(p\Rightarrow q)\vee (\tilde{\ }(q\Rightarrow p))\] (\[\because \]by De-Morgans law) \[=(p\wedge \tilde{\ }q)\vee (q\wedge \tilde{\ }p).\]
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