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Math Help - subset proofs

  1. #1
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    subset proofs

    I am a bit confused on how to do proofs with subsets. Here is an example:

    Suppose you have 4 sets A, B, C, D

    Given A is a subset of B and C is a subset of D, can you prove that (AUC) is a subset of (BUD)? Intuitively, this looks like you can prove it, buy formally I am unsure how to proceed.

    Any help/hints are much appreciated.

    TonD
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by TonD View Post
    I am a bit confused on how to do proofs with subsets. Here is an example:

    Suppose you have 4 sets A, B, C, D

    Given A is a subset of B and C is a subset of D, can you prove that (AUC) is a subset of (BUD)? Intuitively, this looks like you can prove it, buy formally I am unsure how to proceed.

    Any help/hints are much appreciated.

    TonD
    suppose x \in A \cup C now show that x \in B \cup D

    CB
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  3. #3
    MHF Contributor

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    In other words, use the definition of "subset":
    A\subseteq B if and only whenever x\in A, x\in B
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