# Set Theory

• I
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.

member 587159
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.

member 587159
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.

PeroK
Homework Helper
Gold Member
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.

PeroK
Homework Helper
Gold Member
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.