(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

where A and B are sets and ' \ ' means set difference

under what conditions does A \ (A \ B) = B

2. Relevant equations

S\A = {X | X in S and X not in A}

B < A (subset) means if x is in B then x is in A

3. The attempt at a solution

I get that if B is a subset of A then A \ (A \ B) = B. But I don't know how to prove it. Here's my attempt thus far

assume x is in A \ (A \ B)

to be proved x is in B

from assumption x is in A and x is not in (A \ B) , then

x is in A and not { L | L in A and L not in B}

because B is a subset of A

x is in A and . . .

. . .

It's like I know that A \ B contains nothing from B but because A includes B, subtracting it from A will give back B. I don't know how to phrase it right for making a mathematical argument. Any guidance will be strongly appreciated.

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# Homework Help: Real analysis chapter 0

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