- #1

- 5

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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.

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- 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

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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

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

- #6

- 16,657

- 8,575

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

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

- #8

- 16,657

- 8,575

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

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Yes, thank you very much sir.

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