Step 1: Understanding the Question:
The question provides a compound conditional statement that is False and asks for the individual truth values of the component statements.
Step 3: Detailed Explanation:
A conditional statement $X \rightarrow Y$ is False only when the antecedent $X$ is True (T) and the consequent $Y$ is False (F).
Given: $(p \wedge q) \rightarrow (r \vee \neg s) \equiv F$
This implies:
1. $(p \wedge q) \equiv T$
For a conjunction $(\wedge)$ to be True, both component statements must be True.
Therefore, $p \equiv T$ and $q \equiv T$.
2. $(r \vee \neg s) \equiv F$
For a disjunction $(\vee)$ to be False, both component statements must be False.
Therefore, $r \equiv F$ and $\neg s \equiv F$.
Since $\neg s \equiv F$, then $s \equiv T$.
Final truth values: $p = T, q = T, r = F, s = T$.
Step 4: Final Answer:
The truth values are (T, T, F, T).