I am trying to prove that
$p \leftrightarrow q \equiv (p\lor q)\to(p \land q)$
and am really lost in the steps to solve this.
So far I have:
$p \leftrightarrow q \equiv (p\to q)\land(q\to p) \qquad$|equivalence
$p \leftrightarrow q\equiv (\neg p\lor q)\land(\neg q\lor p) \qquad$|implication
and I am not sure how to proceed from here. Any advice would be greatly appreciated!
edit:
Thanks to lord farin i now have
≡ (~p ∨ q) ∧ (q → p) Implication Law
≡ (q → p) ∧ (~p ∨ q) Commutative Law
≡ (q → p ∧ ~p ) ∨ (q → p ∧ q) Distributive Law
≡ (~p ∧ q → p) ∨ (q ∧ q → p) Commutative Law
but i am unsure of how to get there still.