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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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Answer» `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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