$P$: $((p \land q) \vee r)\implies (l \vee t)$... If $p$,$q$,and $l$ are all false and $r$ and $t$ are true determine if $P$ is true.
How would I show this just by logically writing out $p$ and $q$ false or $r$ true implies $l$ false or $t$ true so $P$ is true? Or would I have to make a truth table which would be complicated. $P$ is true right?