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Homework Help: Discrete Mathamatics Proving

  1. Jan 30, 2012 #1
    Prove that (A n B) - C = (A - C) n (B - C).

    n = intersect
    ≠ε = not a member

    I got the first one by doing:
    (xεA ^xεB) ^X≠εC ( by identity law and compliment law)

    where would I go on from now?
  2. jcsd
  3. Jan 30, 2012 #2
    so basically you have to prove the equality of sets. forward way is to let [itex]x\in(A\cap B)\setminus C[/itex] be arbitrary. Then as you have shown

    [tex]x\in A\;x\in B\;\; x\notin C[/tex]

    which means that x is A and not in C AND x is in B and not in C. So just combine that to arrive at the right side. Then proceed to the reverse direction.
  4. Jan 30, 2012 #3
    What do you mean as in "(A∩B)∖C"to be arbitrary and I have to show how it goes from (A∩B) -C to (A-C) ∩ (B-C)
  5. Jan 30, 2012 #4
  6. Jan 30, 2012 #5
    when you have to prove that two sets are equal you have to prove that

    [tex]A\subseteq B\mbox{ and }B\subseteq A[/tex]

    So to prove [itex]A\subseteq B[/itex] you take arbitrary member of A and then prove that
    its also member of B. And similar proof for proving [itex]B\subseteq A[/itex]
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