A) \[\tilde{\ }[p\vee (\tilde{\ }q)]\equiv (\tilde{\ }p)\vee q\]
B) \[[p\vee q]\vee (\tilde{\ }p)\] is a tautology
C) \[[p\wedge q)\wedge (\tilde{\ }p)\] is a contradiction
D) \[\tilde{\ }[p\vee q]\equiv (\tilde{\ }p)\vee (\tilde{\ }q)\]
Correct Answer: D
Solution :
[d] since \[\tilde{\ }(p\vee q)\equiv \tilde{\ }p\wedge \tilde{\ }q\] (By De-Morgan?s? law) \[\therefore \,\,\,\,\tilde{\ }(p\vee q)\ne \,\tilde{\ }p\vee \tilde{\ }q\] \[\therefore \] [d] is the false statement
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