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Prove, $(\mathrm{AVB}) \wedge[(\neg \mathrm{A}) \wedge(\neg \mathrm{B})]$ is a contradiction.
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written 2.1 years ago by
prajapatijaimin
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Solution:
$ \text { To Prove:- }(A \vee B) \wedge[(\neg A) \wedge(\neg B)] \text { is a contradiction. }\\ $
$ \begin{array}{|c|c|c|c|c|c|c|} \hline A & B & A \vee B & \neg A & \neg B & (\neg A) \wedge(\neg B) & (A \vee B) \wedge[(\neg A) \wedge(\neg B)] \\\\ \hline T & T & T & F & F & F & F \\\\ T & F & T & F & T & F & F \\\\ F & T & T & T & F & F & F \\\\ F & F & F & T & T & T & F \\\\ \hline \end{array}\\ $
As we can see that the value of given expression ire.
$(A \vee B) \wedge[(\neg A) \wedge(\neg B)]$,
is False.
Hence, it is a contradiction. Aus.
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