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Math Help - Convex Sets

  1. #1
    Member aldrincabrera's Avatar
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    Smile Convex Sets

    ,.,How should i do this??

    Show that the intersection of two convex sets is convex but the union of convex sets does not have to be convex,.


    thnx
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  2. #2
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    Re: Convex Sets

    The last part is easy by counter example.

    Take x > 0 and y > 0 and

    Set 1 {(x,y)|(y/2) + (x/1) <= 1}
    Set 2 {(x,y)|(y/1) + (x/2) <= 1}
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  3. #3
    A Plied Mathematician
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    Re: Convex Sets

    For the first part, just look at the definition of convex set, and the definition of intersection. What can you do with that?
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  4. #4
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    Re: Convex Sets

    Quote Originally Posted by aldrincabrera View Post
    Show that the intersection of two convex sets is convex but the union of convex sets does not have to be convex,.
    If each of A~\&~B is a convex set and \{p,q\}\subseteq A\cap B then the 'line segment" \overline{pq} is in both sets.

    On the other hand, if p\in A\setminus B\text{ and }q\in B\setminus A what can you say about \overline{pq} with respect to A\cup B~?
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