If the truth value of the compound statement $[(p \vee q) \wedge (q \rightarrow r) \wedge (\sim r)] \rightarrow (p \wedge q)$ is False then the truth values of $p \rightarrow q$ and $q \rightarrow p$ are respectively......

The compound statement $X \rightarrow Y$ is False if and only if $X$ is True and $Y$ is False.

Here, $X = (p \vee q) \wedge (q \rightarrow r) \wedge (\sim r)$ and $Y = p \wedge q$.

Since $X$ is True, each of its components must be True:
1) $\sim r$ is True $\Rightarrow r$ is False.
2) $q \rightarrow r$ is True. Since $r$ is False, $q$ must be False.
3) $p \vee q$ is True. Since $q$ is False, $p$ must be True.

Checking $Y$: $p \wedge q = T \wedge F = F$, which satisfies the condition that $Y$ is False.

Thus, $p = T$ and $q = F$.

Now, we evaluate $p \rightarrow q$ and $q \rightarrow p$:
$p \rightarrow q = T \rightarrow F = F$
$q \rightarrow p = F \rightarrow T = T$

The truth values are $(F, T)$.

Answer: $(F, T)$