Which of the following statements is a contra | vedclass

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(A) statement is a contradiction if its truth value is always false for all possible truth values of its components.Let us evaluate the expression $(p

Vedclass · Accepted Answer

$(p \wedge q) \wedge (\sim (p \vee q))$

Vedclass · Answer

(A) statement is a contradiction if its truth value is always false for all possible truth values of its components.Let us evaluate the expression $(p \wedge q) \wedge (\sim (p \vee q))$.Using De Morgan's Law,$\sim (p \vee q) \equiv (\sim p \wedge \sim q)$.So,the expression becomes $(p \wedge q) \wedge (\sim p \wedge \sim q)$.By associative and commutative laws,this is equivalent to $(p \wedge \sim p) \wedge (q \wedge \sim q)$.Since $(p \wedge \sim p)$ is always false $(F)$ and $(q \wedge \sim q)$ is always false $(F)$,the entire expression is $F \wedge F$,which is always $F$.Therefore,$(p \wedge q) \wedge (\sim (p \vee q))$ is a contradiction.

Which of the following statements is a contradiction?

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