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(C) Step $1$: Simplify the given expression $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q)$.Step $2$: Use the distributive law on

Vedclass · Accepted Answer

$T, T$

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(C) Step $1$: Simplify the given expression $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q)$.Step $2$: Use the distributive law on the first two terms: $(\sim p \land (q \lor \sim q)) \lor (p \land \sim q)$.Step $3$: Since $(q \lor \sim q) \equiv T$, the expression becomes $(\sim p \land T) \lor (p \land \sim q) \equiv \sim p \lor (p \land \sim q)$.Step $4$: Apply the distributive law again: $(\sim p \lor p) \land (\sim p \lor \sim q) \equiv T \land (\sim p \lor \sim q) \equiv \sim p \lor \sim q$.Step $5$: Given the truth value is $F$, we have $\sim p \lor \sim q \equiv F$. This implies $\sim p \equiv F$ (so $p \equiv T$) and $\sim q \equiv F$ (so $q \equiv T$).Step $6$: Evaluate $(p \lor \sim q) \equiv (T \lor \sim T) \equiv (T \lor F) \equiv T$.Step $7$: Evaluate $(p 	o q) \equiv (T 	o T) \equiv T$.Step $8$: The truth values are $T, T$.

If the truth value of the statement pattern $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q)$ is $F$, then the truth values of $(p \lor \sim q)$ and $(p \to q)$ are respectively.

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