So I have been looking at this question all day and have made a few attempts but can't seem to get any further.
Can someone please help with me proving this algebra equation and what laws I would need to use?
Forgive me for not knowing how to use the proper symbols on this. first time here, Didn't even know there was a forum for this.
I have also looked through already answered questions, and could not find anything similar.
This is the equation I need to prove
$p \leftrightarrow q \equiv (p \lor q) \rightarrow (p \land q)$
So far I have
$ p \leftrightarrow q \equiv (p \to q) \land (q \to p) $ The Equivalence Law
$(p \to q) \land (q \to p) \equiv (\lnot p \lor q) \land (\lnot q \lor p) $ Implication Law
$(\lnot p \lor q) \land (\lnot q \lor p) \equiv (p \land q) \lor (\lnot p \land \lnot q) $ not sure what law(I used a truth table)
I am not sure if I am even on the right track but if I am, when does it become proved? I think I may need like 3 or 4 more laws to be used.