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I.If AB, then show that AUBB (use Venn diagram). |
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Answer» A is a subset of B, then every element of A is an element of B. We need to prove that A union B = B. This is an equality of sets, so we must prove that every element of each set must be in the other set. Suppose x is in B. Then clearly x is in A union B. Suppose x is in A union B. Then x is in A or x is in B. If x is in B, we are done. If x is in A, then since A is a subset of B, x is also in B. Either way, x is in B, and we are done. Therefore A union B = B. |
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