A) \[(\tilde{\ }p\vee q)\wedge \tilde{\ }q\]
B) \[(p\wedge \tilde{\ }q)\vee q\]
C) \[(\tilde{\ }p\wedge q)\vee \tilde{\ }q\]
D) \[(p\wedge \tilde{\ }q)\vee \tilde{\ }q\]
Correct Answer: C
Solution :
[c] \[\tilde{\ }\{(p\vee (\tilde{\ }q))\wedge q\}=(\tilde{\ }(p\vee (\tilde{\ }q)))\vee (\tilde{\ }q)\] By De Morgan?s Law, \[\tilde{\ }(A\wedge B)=(\tilde{\ }A)\vee (\tilde{\ }B)\] \[=((\tilde{\ }p)\wedge (\tilde{\ }(\tilde{\ }q)))\vee (\tilde{\ }q)\] [Using De Morgan?s law again] \[=(\tilde{\ }p\wedge q)\vee (\tilde{\ }q)\] \[[\because \tilde{\ }(\tilde{\ }q)=q]\]
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