I have a 'homework' problem which I'd like some help on. It's a proof. It's awfully simple but the only problem is that I'm not sure how exactly one should approach it especially if one is looking to give a 'slick' proof.
It goes like this:
Prove that for subsets A, B c X:
A c B <=> A U B = B <=> A ^ B = A <=> B' c A'
where: c:= subset
U:= union
^:= intersection
My request is for some help on how to go about using the logical equivalence symbol in proving the above equivalences. I have constructed a 'scrappy' and lengthy proof but would like to achieve brevity in expression.
Would really appreciate if somebody, without giving the actual proof, helped me with how to proceed.
