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Homework Help: 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


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    Science Advisor

    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


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    Gold Member

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