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.