I gotta draw $p \lor q ↔ q$ from $p → q$, logically. not by a truth table.
While it seems obvious, I cannot find a formal proof.
This is how far I came up to:
$\quad p \lor q$
$\equiv (p \land T) \lor q$
$\equiv q \lor (p \land T)$
$\equiv (q \lor p) \land (q \lor T)$
$\equiv (q \lor p) \land T$
$\equiv (q \lor p) \land (\neg p \lor q)$
I know that by drawing a venn-diagram here i can intuitively know that it is equivalent to q, but how do I draw such conclusion logically?