# Set Theory

• I

## Main Question or Discussion Point

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.

Math_QED
Homework Helper
2019 Award
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.

Math_QED
Homework Helper
2019 Award
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