Which of the following statement patterns is | vedclass

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(A) statement pattern is a contradiction if its truth value is $F$ for all possible truth values of its components.We analyze $S_{1} \equiv (p \righta

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$S_{1}$

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(A) statement pattern is a contradiction if its truth value is $F$ for all possible truth values of its components.We analyze $S_{1} \equiv (p \rightarrow q) \wedge (p \wedge \sim q)$.Using logical laws:$S_{1} \equiv (\sim p \vee q) \wedge (p \wedge \sim q)$$S_{1} \equiv [(\sim p \vee q) \wedge p] \wedge \sim q$$S_{1} \equiv [(\sim p \wedge p) \vee (q \wedge p)] \wedge \sim q$$S_{1} \equiv [F \vee (p \wedge q)] \wedge \sim q$$S_{1} \equiv (p \wedge q) \wedge \sim q$$S_{1} \equiv p \wedge (q \wedge \sim q)$$S_{1} \equiv p \wedge F$$S_{1} \equiv F$Since the truth value is always $F$,$S_{1}$ is a contradiction.

Which of the following statement patterns is a contradiction?
$S_{1} \equiv (p \rightarrow q) \wedge (p \wedge \sim q)$
$S_{2} \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$
$S_{3} \equiv (p \vee q) \rightarrow \sim p$
$S_{4} \equiv [p \wedge (p \rightarrow q)] \leftrightarrow q$

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Which of the following statement patterns is a contradiction?$S_{1} \equiv (p \rightarrow q) \wedge (p \wedge \sim q)$$S_{2} \equiv [p \wedge (p$ $\rightarrow q)]$ $\rightarrow q$$S_{3} \equiv (p \vee q) \rightarrow \sim p$$S_{4} \equiv [p \wedge (p \rightarrow q)] \leftrightarrow q$