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Homework Help: Discrete Math problem please help!

  1. Feb 25, 2010 #1
    One of my homework problems says is this true or false and prove your answer:

    For all sets A, B, C if A n C is a subset of B n C then A is a subset of B.

    I believe the answer is true but i have no idea please help!
     
  2. jcsd
  3. Feb 25, 2010 #2

    vela

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    What are the definitions of subset and intersection?
     
  4. Feb 25, 2010 #3
    If A is a subset of B that means that if there is an element x in A then x is also an elemnt of B. And A n B means x is an element of A and B
     
  5. Feb 25, 2010 #4

    vela

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    Good! So assume [itex]x\in A[/itex]. You want to show that [itex]x \in B[/itex]. All you know is that [itex]A \cap C \in B \cap C[/itex].

    If you run into problems proving it, you may realize the problem is there because it's a counterexample of what you're trying to prove.
     
  6. Feb 26, 2010 #5
    Consider
    [tex]A = \{ 1, 3 \}[/tex]
    [tex]B = \{ 1, 2, 4 \}[/tex]
    [tex]C = \{ 1, 2 \}[/tex]
     
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