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Math Help - Set Proofs

  1. #1
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    Set Proofs

    Let A and B be sets. Show that ( A ∩ B) ⊆ A. Prove first the left side ⊆ right side. Then right side ⊆ left side.
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    Is this a true statement x\in A\rightarrow x\in A?
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  3. #3
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    yes
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    So if x\in A\cap B then x\in A\text{ and }x\in B. Thus ?
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    Then they are subsets
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    You don't need to prove right to left, and we can't anyway.
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  7. #7
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    Quote Originally Posted by lm6485 View Post
    Then they are subsets
    Yes, but say specifically what you mean by "they", and say why "x in A and x in B" justifies that (it might be so obvious that you miss the need to say it).
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