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Proving a set identity

  1. Feb 7, 2014 #1
    1. The problem statement, all variables and given/known data

    9DXjR4I.png

    2. Relevant equations

    I have to use these set identities:

    rD3CeXi.png

    hW9GJqA.png

    REAXX4U.png

    3. The attempt at a solution

    Pretty sure this is impossible because there's no identity for the Cartesian product.
     
  2. jcsd
  3. Feb 7, 2014 #2
    Just go at it the old fashion way.

    Suppose (a, d) [itex]\in[/itex] A X (B [itex]\cup[/itex] C). Then a [itex]\in[/itex] A. Also d [itex]\in[/itex] B or d [itex]\in[/itex] C. So (a,d) [itex]\in[/itex] (A X B) or (a,d) [itex]\in[/itex] (A X C).

    Thus (a,d) [itex]\in[/itex] (A X B) [itex]\cup[/itex] (A X C).

    Therefore A X (B [itex]\cup[/itex] C) [itex]\subseteq[/itex] (A X B) [itex]\cup[/itex] (A X C).

    Proving the subset goes the other way follows similarly.
     
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