# I Set Theory

1. Jun 14, 2016

### 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.

2. Jun 14, 2016

### Math_QED

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}

3. Jun 14, 2016

### 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.

4. Jun 14, 2016

### Math_QED

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

5. Jun 14, 2016

### Chis96

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

6. Jun 14, 2016

### PeroK

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.

7. Jun 14, 2016

### Chis96

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

8. Jun 14, 2016

### PeroK

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

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

9. Jun 14, 2016

### Chis96

Yes, thank you very much sir.