Consider the statement patterns:A. (q to p) l | vedclass

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

Vedclass · Accepted Answer

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

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(B) Step $1$: Analyze $A: (q 	o p) \lor (p 	o q) \equiv (\sim q \lor p) \lor (\sim p \lor q) \equiv (\sim q \lor q) \lor (\sim p \lor p) \equiv T \lor T \equiv T$. Thus, $A$ is a tautology.Step $2$: Analyze $B: (\sim p \lor \sim q) \leftrightarrow \sim (p \land q)$. By De Morgan's Law, $\sim p \lor \sim q \equiv \sim (p \land q)$. Thus, $B$ is $X \leftrightarrow X$, which is a tautology.Step $3$: Analyze $C: [(p \lor q) \land \sim p] \land \sim q \equiv [(p \land \sim p) \lor (q \land \sim p)] \land \sim q \equiv [F \lor (q \land \sim p)] \land \sim q \equiv (q \land \sim p) \land \sim q \equiv (q \land \sim q) \land \sim p \equiv F \land \sim p \equiv F$. Thus, $C$ is a contradiction.Step $4$: Analyze $D: (p \land q) \land (\sim p \lor \sim q) \equiv (p \land q) \land \sim (p \land q) \equiv F$. Thus, $D$ is a contradiction.Conclusion: $A$ and $B$ are tautologies, $C$ and $D$ are contradictions.

Consider the statement patterns:
$A. (q \to p) \lor (p \to q)$
$B. (\sim p \lor \sim q) \leftrightarrow \sim (p \land q)$
$C. [(p \lor q) \land \sim p] \land \sim q$
$D. (p \land q) \land (\sim p \lor \sim q)$
Then identify the nature of these statement patterns.

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Consider the statement patterns:$A. (q \to p) \lor (p \to q)$$B. (\sim p \lor \sim q) \leftrightarrow \sim (p \land q)$$C. [(p \lor q) \land \sim p] \land \sim q$$D. (p \land q) \land (\sim p \lor \sim q)$Then identify the nature of these statement patterns.