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Homework Help: Proving equalities with operations on sets

  1. Jan 20, 2010 #1
    1. The problem statement, all variables and given/known data
    Let A, B, C be any sets.

    Prove that if [tex]C\subseteq A[/tex], then [tex](A\cap B)\cup C[/tex] = [tex]A\cap (B\cup C)[/tex]

    2. Relevant equations


    3. The attempt at a solution

    Don't even know where to begin, If someone could point me in the right direction, that would be the best.
  2. jcsd
  3. Jan 20, 2010 #2


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    To prove two sets A and B are equal, you need to show [itex]A\subset B[/itex] and [itex]B\subset A[/itex].
  4. Jan 20, 2010 #3
    Thankyou! I think I'm on the right track, I see how that would make both sides equal only if C is a subset of A.
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