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Math Help - Finite Set

  1. #1
    Senior Member slevvio's Avatar
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    Finite Set

    Let U be a finite set and V a subset of U.

    Prove that |U \ V| = |U| - |V|

    I can see this in my head and if i draw a picture but how do i prove it? thanks for any help
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  2. #2
    MHF Contributor

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    Take note of two facts:
    U = \left( {U\backslash V} \right) \cup V\;\& \;A \cap B = \emptyset \; \Rightarrow \;\left| {A \cup B} \right| = \left| A \right| + \left| B \right|
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