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If A and B are two sets, then prove that...

If A and B are two sets, then prove that the sets A - B, B - A and `A cap B` are mutually disjoint.

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`A - B={x:x in A and x in B}`
`B-A={x:x in B and x in A}`
` : A- B and B -A` are mutually disjoint
Now, `x in A - B rArr x in A and x in B`
`rArr x cancel(in) A cap B`
`:. A- B and A cap B` are mutually disjoint.
Similarly, we can prove that `B - A adn A cap B` are mutually disjoint
Therefore, `A - B, B-A and A cap B` are mutually disjoint sets.
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