A) \[p\Rightarrow q\equiv \ \tilde{\ }p\Rightarrow \ \tilde{\ }q\]
B) \[\tilde{\ }(p\Rightarrow \ \tilde{\ }q)\equiv \ \tilde{\ }p\wedge q\]
C) \[\tilde{\ }(\tilde{\ }p\Rightarrow \,\tilde{\ }q)\equiv \tilde{\ }p\wedge q\]
D) \[\tilde{\ }(p\Leftrightarrow q)\equiv [\tilde{\ }(p\Rightarrow q)\wedge \tilde{\ }(q\Rightarrow p)]\]
Correct Answer: C
Solution :
\[\tilde{\ }(p\Rightarrow q)\equiv p\ \wedge \tilde{\ }q\] \ \[\tilde{\ }(\tilde{\ }p\Rightarrow \ \tilde{\ }q)\equiv \ \tilde{\ }p\ \wedge \tilde{\ }(\tilde{\ }q)\equiv \ \tilde{\ }p\wedge q\] Thus \[\tilde{\ }(\tilde{\ }p\Rightarrow \ \tilde{\ }q)\equiv \ \tilde{\ }p\wedge q\].
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