1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Discrete Mathamatics Proving
  1. Proving a discrete sum (Replies: 7)