$A$. For any propositions P and Q, the following is always true: $(P \rightarrow Q) \vee (Q \rightarrow P).$
$\text{Proof}$:
Here's one way to see this. If $Q$ is true, then $P \rightarrow Q$ is true because anything implies a true statement. If $Q$ is false, then $Q \rightarrow P$ is true because false implies anything. (If this is confusing, you should review the truth table for $\rightarrow !$)
$B$. For any propositions $P, Q$, and $R$, the following statement is always true: $(P \rightarrow Q) \vee (Q \rightarrow R).$
$\text{Proof}$ :
This is basically the same argument as before. If $Q$ is true, then $P \rightarrow Q$
is true because anything implies a true statement. If $Q$ is false, then $Q \rightarrow R$ is true because false implies anything.
Of all the connectives we've seen, the $\rightarrow$ connective is probably the trickiest. We asked this question to force you to disentangle notions of correlation or causality from the behavior of the $\rightarrow$ connective.