In boolean algebra, having trouble reducing (¬a∨b)∧(¬b∨a).

Question

Starting with (¬a∨b)∧(¬b∨a), I'm having trouble reducing this to: (a∨b)⟹(a∧b)

I am lost with what is the next step after (¬a∨b)∧(¬b∨a). Is it this perhaps?:

¬(¬a∨b)∧¬(¬b∨a) ? And then work on from there?

Answer 1

First "FOIL" it (i.e. use the distributive property twice) to get $$(\lnot a \land \lnot b)\lor(\lnot a\land a)\lor(b\land\lnot b)\lor(b\land a).$$ The middle terms are zero so go away and then just use Demorgan on the first to get $$ \lnot(a\lor b) \lor (b\land a)$$ which is the same thing as $$ (a\lor b)\Rightarrow(a\land b)$$