1. ## Set Theory Q

Hi I need help with the following:

1.
For any sets A and B, prove that:
a) A = (A ∩ B) or (A\B)
b) (A\B) or (B\A) = (A or B)\(A∩B)

2. For any sets A,B,C, prove that if
A\(B or C) = (A\B)or(A\C), then A∩(B or C) ⊆ A∩B∩C

3. For any sets A and B, prove that A\(A\B) = A∩B

4. Prove that if A\(B\C) ⊆ (A\B)\C then A∩C = 0

Any or all would be much appreciated!

anyone?

3. ## Re: Set Theory Q

Originally Posted by DirectorRico
For any sets A and B, prove that:
a) A = (A ∩ B) or (A\B)
b) (A\B) or (B\A) = (A or B)\(A∩B)
2. For any sets A,B,C, prove that if
A\(B or C) = (A\B)or(A\C), then A∩(B or C) ⊆ A∩B∩C
3. For any sets A and B, prove that A\(A\B) = A∩B
4. Prove that if A\(B\C) ⊆ (A\B)\C then A∩C = 0

DO NOT BUMP.

You first question is meaningless.

$\displaystyle (A\setminus B)\cup(B\setminus A)=(A\cap B^c)\cup(B\cap A^c)$ EXPAND.

$\displaystyle A\setminus(B\setminus C)=(A\cap (B\setminus C)^c=A\cap (B^c\cup C)$

AND $\displaystyle (A\setminus B)\setminus C=(A\cap B^c)\cap C^c$

4. ## Re: Set Theory Q

My mistake.

Could you possibly answer #2,#3 or #4?

5. ## Re: Set Theory Q

Originally Posted by DirectorRico
Could you possibly answer #2,#3 or #4?

I did answer each of those.
You have to do the work.

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