1. Not finding help here? Sign up for a free 30min 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 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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Discrete Math: prove an intersection from a given
Loading...