Proof Help: Prove (A∪B)-C ⊆ A∪(B-C)

[Ja6464]

I am stuck on a proof question:

Prove (A∪B)-C ⊆ A∪(B-C)

If anyone would be able to help me with this proof it would be much appreciated, as I have an exam on this topic tomorrow afternoon!

Thanks a lot.

 

[dodo]

In a proof like this (checking if a set is included into another) you typically take one arbitrary element x from the first set, and prove that it also belongs to the second set. (So any element from the first is included in the second, so the first set is a subset of the second.)

If x is in the first set, then it is either in A or in B (or both), but certainly not in C. Try to figure out each of the two cases (x in A, x in B), and see if, in both cases, x belongs to the second set.

Hope this helps.

 

[Ja6464]

Thank you that's helped a lot, I think I've managed to prove it now.

Hopefully I can do it again tomorrow!