If A is subset of B then find A intersection B , A union B ,A-B

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If A is subset of B then find A intersection B , A union B ,A-B

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Elliana 1 month 2021-08-16T05:27:27+00:00 1 Answer 0 views 0

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    2021-08-16T05:29:13+00:00

    Step-by-step explanation:

    The trivial case first: If A⊆B and A=∅, then A∩B=∅=A. Conversely, if A∩B=A and A=∅, then A⊆B, since ∅ is a subset of every set.

    Now, suppose A≠∅. Suppose A⊆B. If x∈A, then , from the definition of subset. Thus,  and . Therefore, by the definition of intersection of sets, . Therefore, every  in  is in . From the definition of containment, . Each element of  is in both  and , so . Since  and , the definition of set equality gives . For the converse. If , then since , . Q.E.D.

    Now, write it up nicely in your own hand before turning it in.

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