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) \[\tilde{\ }(\tilde{\ }p\Leftrightarrow q)\equiv [\tilde{\ }(p\Rightarrow q)\wedge \tilde{\ }(q\Rightarrow p)]\]
Correct Answer: C
Solution :
[c] \[\tilde{\ }(p\Rightarrow q)\equiv p\wedge \tilde{\ }q\] \[\therefore \tilde{\ }(\tilde{\ }p\Rightarrow \tilde{\ }q)\equiv \tilde{\ }p\wedge \tilde{\ }(\tilde{\ }q)\equiv \tilde{\ }p\wedge q\] Thus \[\tilde{\ }(\tilde{\ }p\Rightarrow \tilde{\ }q)\equiv \,\tilde{\ }p\wedge q\]
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