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 $(p \rightarrow q) \Rightarrow [(p \vee r) \rightarrow (q \vee r)]$: