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

[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.

 

[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}

 

[Chis96]

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?

 

[Chis96]

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

 

[PeroK]

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.

 

[Chis96]

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

 

[PeroK]

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.

 

[Chis96]

Yes, thank you very much sir.