# How to prove this equality using boolean algebra?

I have approximately no idea on how to solve the following problem, so any help would very much be appreciated:

$$x' y'+ x y = (x y' + x' y)'$$

I can't figure out how to prove the equalities using boolean algebra
Here's one way. First, use DeMorgan's law: $$(xy' + x'y)' = (xy')'(x'y)' = (x' + y)(x + y')$$ From there, you can expand the product using the distributive property, noting that $x'x$, which means "$x$ and not $x$", is $0$ (i.e. false). $$(x' + y)(x + y') = (x'x) + xy + x'y' + (yy') = xy + x'y'$$