- #1

- 5

- 0

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.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- I
- Thread starter Chis96
- Start date

- #1

- 5

- 0

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

member 587159

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

A\B = {x|x ∈ A and x ∉ B}

- #3

- 5

- 0

Well.... there are no definitions, it just says let A, B and C be any set, prove that A\B⊂A.

- #4

member 587159

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

- #5

- 5

- 0

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

- #6

- 21,594

- 12,890

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.

- #7

- 5

- 0

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

- #8

- 21,594

- 12,890

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.

- #9

- 5

- 0

Yes, thank you very much sir.

Share: