If the truth value of the compound statement | vedclass

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(B) Step $1$: Analyze the given implication. An implication $A 	o B$ is false only when $A$ is $T$ and $B$ is $F$.Step $2$: Here, $A = [(p \leftright

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$(T, F)$

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(B) Step $1$: Analyze the given implication. An implication $A 	o B$ is false only when $A$ is $T$ and $B$ is $F$.Step $2$: Here, $A = [(p \leftrightarrow q) \land (q 	o r) \land \sim r]$ and $B = (p \land \sim q)$. Since $B$ is false, $(p \land \sim q)$ is $F$.Step $3$: Since $A$ is true, all components must be true: $(p \leftrightarrow q) = T$, $(q 	o r) = T$, and $\sim r = T$. Thus, $r = F$.Step $4$: Since $(q 	o r) = T$ and $r = F$, $q$ must be $F$ (because $T 	o F$ is $F$).Step $5$: Since $(p \leftrightarrow q) = T$ and $q = F$, $p$ must be $F$.Step $6$: Evaluate the first pattern: $(p 	o q) \leftrightarrow (q 	o r) = (F 	o F) \leftrightarrow (F 	o F) = T \leftrightarrow T = T$.Step $7$: Evaluate the second pattern: $\sim (p \lor r) 	o (q \land p) = \sim (F \lor F) 	o (F \land F) = \sim F 	o F = T 	o F = F$.Step $8$: 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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