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Precalculus Mathematics Homework Help
Understanding Set Operations: A Closer Look at A ∖ (A ∖ B) = A ∩ B
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[QUOTE="member 587159, post: 6393755"] Well, I think you are going in the right direction. But a real formal proof (at this level) requires more details. Typically, when showing that two sets ##X,Y## are equal, you show that ##X \subseteq Y## and ##Y\subseteq X##. Showing ##X\subseteq Y## can be done by fixing an arbitrary element ##x\in X## and then after some steps deducing that ##x \in Y##. Similarly, you show ##Y \subseteq X##. So, let us try this on your case: Let ##x \in A\setminus (A \setminus B)##. Then ##x\in A## and ##x \notin A \setminus B##. The latter means that ##x\notin A## or that ##x\in B##, but we already know that ##x\in A## so we must have ##x\in B##. Hence, ##x\in A## and ##x\in B##, which means ##x\in A \cap B##. Can you try the other direction yourself now? Two additional remarks: (1) Try to write a more descriptive title for your question. For example, "Prove the set equality ##A\cap B = A \setminus (A \setminus B)##" (2) Your first line in your post contains some typos. [/QUOTE]
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Precalculus Mathematics Homework Help
Understanding Set Operations: A Closer Look at A ∖ (A ∖ B) = A ∩ B
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