Consider the following statement patterns:A. | vedclass

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(B) Step $1$: Analyze $A$: $(q 	o p) \vee (p 	o q) \equiv (\sim q \vee p) \vee (\sim p \vee q) \equiv (\sim q \vee q) \vee (\sim p \vee p) \equiv T

Vedclass · Accepted Answer

$A$ and $B$ are tautologies, $C$ and $D$ are contradictions.

Vedclass · Answer

(B) Step $1$: Analyze $A$: $(q 	o p) \vee (p 	o q) \equiv (\sim q \vee p) \vee (\sim p \vee q) \equiv (\sim q \vee q) \vee (\sim p \vee p) \equiv T \vee T \equiv T$. Thus, $A$ is a tautology.Step $2$: Analyze $B$: By De Morgan's Law, $\sim (p \wedge q) \equiv \sim p \vee \sim q$. Thus, $(\sim p \vee \sim q) \leftrightarrow (\sim p \vee \sim q)$ is always true. Thus, $B$ is a tautology.Step $3$: Analyze $C$: $[(p \vee q) \wedge \sim p] \wedge \sim q \equiv [(p \wedge \sim p) \vee (q \wedge \sim p)] \wedge \sim q \equiv [F \vee (q \wedge \sim p)] \wedge \sim q \equiv (q \wedge \sim p \wedge \sim q) \equiv (q \wedge \sim q) \wedge \sim p \equiv F \wedge \sim p \equiv F$. Thus, $C$ is a contradiction.Step $4$: Analyze $D$: $(p \wedge q) \wedge (\sim p \vee \sim q) \equiv (p \wedge q \wedge \sim p) \vee (p \wedge q \wedge \sim q) \equiv (p \wedge \sim p \wedge q) \vee (p \wedge q \wedge \sim q) \equiv (F \wedge q) \vee (p \wedge F) \equiv F \vee F \equiv F$. Thus, $D$ is a contradiction.

Consider the following statement patterns:
$A$. $(q \to p) \vee (p \to q)$
$B$. $(\sim p \vee \sim q) \leftrightarrow \sim (p \wedge q)$
$C$. $[(p \vee q) \wedge \sim p] \wedge \sim q$
$D$. $(p \wedge q) \wedge (\sim p \vee \sim q)$
Which of the following is correct?

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Consider the following statement patterns:$A$. $(q \to p) \vee (p \to q)$$B$. $(\sim p \vee \sim q) \leftrightarrow \sim (p \wedge q)$$C$. $[(p \vee q) \wedge \sim p] \wedge \sim q$$D$. $(p \wedge q) \wedge (\sim p \vee \sim q)$Which of the following is correct?