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Prove the Int<ABC is a convex set.

  1. Mar 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove the Int<ABC is a convex set.

    2. Relevant equations



    3. The attempt at a solution

    1. Int <ABC = H(A,BC) intersect H(C,AB) by the definition of interior.
    2. H(A,BC) is convex and H(C,AB) is convex by Half-Plane Axioms

    I know I need to show the intersection of the two half planes is convex but I do not know how to do this.
     
  2. jcsd
  3. Mar 29, 2012 #2

    HallsofIvy

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    It would help if you would tell us what "ABC" is! Are "A", "B", "C" points and "ABC" the region bounded by the triangle with those vertices?
     
  4. Mar 29, 2012 #3

    Office_Shredder

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    Regardless of the notation, once you get to
    Prove in general that the intersection of two convex sets is convex
     
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