Why a truncated table for logic implication $(p\wedge q) \implies p$ verification? The book Discrete Mathematics by Kenneth A. Ross says: "Let's verify the logic implication $(p\wedge q) \implies p$. For that, we need to consider only just the case when $p\wedge q$ is true; i.e., both, $p$ and $q$, are true. This gives us the truncated table:"

"
Why the author considers that portion of the truth table? What reasoning I must understand to follow that validation technique?
N.B.: The same technique is applied to $(p \rightarrow q) \Rightarrow [(p \vee r) \rightarrow (q \vee r)]$:


Recall that an implication $R\implies S$ is "automatically true" in cases where the hypothesis $R$ is false.  So the only interesting cases to check are those for which the hypothesis is true.
In this case the hypothesis is $p \wedge q$, so you can proceed just with analyzing what would be implied by that being true.
