Hello matthayzon89The union of two sets and is the set of elements that are in or in . Using Set and Logic notation, this means thatNext, note that to prove two sets and are equal, we usually show that and .
So here you'll need to show that(i)and
(ii)Now we prove that by proving that . So we start the proof of (i) with:
So we have now proved (i) that:, from the definition of union, above
, since is False for all
For (ii), for all sets :In particular, when :, again using the definition of union, above
And that completes the proof.