A) \[p\wedge q\]
B) \[p\leftrightarrow q\]
C) \[\tilde{\ }p\vee q\tilde{\ }q\]
D) \[\tilde{\ }p\wedge \tilde{\ }q\]
Correct Answer: D
Solution :
\[\tilde{\ }(p\vee (\tilde{\ }p\wedge q))\] \[=\tilde{\ }p\wedge \tilde{\ }(\tilde{\ }p\wedge q)\] \[=\tilde{\ }p\wedge (p\vee \tilde{\ }q)\] \[=(\tilde{\ }p\wedge p)\vee (\tilde{\ }p\wedge \tilde{\ }q)\] \[=c\vee (\tilde{\ }p\wedge \tilde{\ }p)\] \[=(\tilde{\ }p\wedge \tilde{\ }q)\]
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