I've been working on these problems and unfortunately i cant make heads or tails of these two.(adsbygoogle = window.adsbygoogle || []).push({});

Any insight where to start the proof would be great.

1)Let A, B and C be sets. Show that if A~B⊆C, then A~C⊆B holds.

What I got so far:

Is it correct to state that A~B = A⋂B' and A~C = A⋂C'

and my target goal should be to prove that A⋂B'⊆A⋂C' and A⋂C'⊆A⋂B'?

2)If A and B are two non-empty subsets (of the same universe U), then A⋂B≠∅ or B⊆A'.

This i just don't understand how to start a proof of that. Its an OR statement does it suffice to say either condition is true? Doesnt seem much of a proof is you could simply state:

Since A and B are non-empty there are elements in it... namely x which belongs to A and B thus A⋂B≠∅

or

there is an x that belongs to B and B is a subset of A' which A' is U~A, since B is in U then B is a subset of A'

is it that simple or am i missing something? Many thanks

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# Set theory proofs troubles

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