# Proving Set Relationships: A-B ⊂ A & (A∩B)c = A∪Bc

• I
• Chis96

#### Chis96

Can some please explain to me how to solve these two questions?
Let A, B and C be any sets, prove that:
(a) A-B ⊂ A
(b) (A∩B) complement = A complement ∪ B and (A∪B) complement = A complement∩ B complement.

We usually write out A\B instead of A -B

Anyway, start to write down the definitions and see where you get.

A\B = {x|x ∈ A and x ∉ B}

Thank you very much for the correction.
Well... there are no definitions, it just says let A, B and C be any set, prove that A\B⊂A.

Well, look up the definitions! How can you prove something without knowing what the definitions are?

No definitions bro, just have to use x to prove it... That's why I'm confused.

No definitions bro, just have to use x to prove it... That's why I'm confused.

He's talking about the definition of "subset"! As in, what does ##A-B \subset A## actually mean? You can't prove it unless you know what it means.

oh... okay basically what it means is that all elements of A\B are contained inside A.

oh... okay basically what it means is that all elements of A\B are contained inside A.

Yes, although more simply and consistently you could say it means:

Each element of A\B is an element of A.

Yes, thank you very much sir.