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Discrete Math: prove an intersection from a given

  1. Oct 10, 2012 #1
    Discrete Math: prove B intersection A = A, given A-B = null set

    1. Problem Statement:
    Prove B [itex]\cap[/itex] A = A, given A-B = ∅ (empty set)

    3. The attempt at a solution
    xε(B[itex]\cap[/itex]A) => xεB and xεA => Logic given A-B = ∅ => xεA

    I tried using A-B = A[itex]\cap[/itex]!B for xε(A[itex]\cap[/itex]!B)=∅ => xεA and x not in !B or x not in A and Xε!B

    I am unsure how to fill in that logic section and prove that B[itex]\cap[/itex]A=A
    Last edited: Oct 10, 2012
  2. jcsd
  3. Oct 10, 2012 #2
    The first direction is fine. If x is in A[itex]\bigcap[/itex]B then, certainly, x is in A (no need to use the given statement). Now suppose that x is in A and proceed by contradiction (to show that x is in A[itex]\bigcap[/itex]B). If x is not also in B determine what that implies about the given statement.
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