A) \[(\tilde{\ }q\wedge r)\to \tilde{\ }p\]
B) \[(q\to r)\to \tilde{\ }p\]
C) \[(q\vee \tilde{\ }r)\to \tilde{\ }p\]
D) None of these
Correct Answer: A
Solution :
[a] We know that the contrapositive of \[p\to q\] is \[\tilde{\ }q\to \tilde{\ }p.\] so contra positive of \[p\to (\tilde{\ }q\to \tilde{\ }r)\] is \[\tilde{\ }(\tilde{\ }q\to \tilde{\ }r)\to \tilde{\ }p\equiv \tilde{\ }q\wedge [\tilde{\ }(\tilde{\ }r)]\tilde{\ }p\] \[\because \,\,\,\,\tilde{\ }(p\to q)\equiv p\wedge \tilde{\ }q\equiv \tilde{\ }q\wedge r\to \tilde{\ }p\]
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