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(B) Step $1$: Analyze the given implication $[(p \leftrightarrow q) \land (q 	o r) \land \sim r] 	o (p \land \sim q) = F$. An implication is false o

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$(T, F)$

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(B) Step $1$: Analyze the given implication $[(p \leftrightarrow q) \land (q 	o r) \land \sim r] 	o (p \land \sim q) = F$. An implication is false only when the antecedent is $T$ and the consequent is $F$.Step $2$: Consequent $(p \land \sim q) = F$. Antecedent $[(p \leftrightarrow q) \land (q 	o r) \land \sim r] = T$. This implies $(p \leftrightarrow q) = T$, $(q 	o r) = T$, and $\sim r = T$.Step $3$: From $\sim r = T$, we get $r = F$. Since $(q 	o r) = T$ and $r = F$, $q$ must be $F$. Since $(p \leftrightarrow q) = T$ and $q = F$, $p$ must be $F$.Step $4$: Evaluate the first pattern $(p 	o q) \leftrightarrow (q 	o r)$. Substituting $p=F, q=F, r=F$: $(F 	o F) \leftrightarrow (F 	o F) \equiv T \leftrightarrow T = T$.Step $5$: Evaluate the second pattern $\sim (p \lor r) 	o (q \land p)$. Substituting $p=F, q=F, r=F$: $\sim (F \lor F) 	o (F \land F) \equiv \sim F 	o F \equiv T 	o F = F$.Step $6$: The truth values are $(T, F)$.

If the truth value of the compound statement $[(p \leftrightarrow q) \land (q \to r) \land \sim r] \to (p \land \sim q)$ is false, then the truth values of the statement patterns $(p \to q) \leftrightarrow (q \to r)$ and $\sim (p \lor r) \to (q \land p)$ are, respectively ...

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