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Convex region

  1. Mar 11, 2017 #1
    1. The problem statement, all variables and given/known data

    Screen_Shot_2017_03_11_at_5_17_08_PM.png
    2. Relevant equations


    3. The attempt at a solution
    Consider S = {(1,1)} and T = {(0,0)}
    Clearly, S and T is convex
    S + T = S and S - T = S
    So both of them are convex.
    So answer is (E)

    But i feel that the answer is too simple....and seems that i wrongly interpreted the question ....
    Any thoughts?
     
  2. jcsd
  3. Mar 11, 2017 #2

    fresh_42

    Staff: Mentor

    What if you choose ##T=\{(2,2)\}\,##? I assume the statement has to be true for any choice of ##S,T##. And it didn't say, that they have to be convex. More interesting is if ##S,T## are balls (or squares, which are easier to handle in this case) of different radius and centers, what can be said then? Can this be generalized to convex sets with a non-empty interior?
     
  4. Mar 11, 2017 #3
    In the last line of the question, "Which of these is TRUE FOR ALL CONVEX SETS S & T? "

    And, even if for only one choice of vertices, S & T both are convex, other options can be eliminated. Right ?
     
  5. Mar 11, 2017 #4

    fresh_42

    Staff: Mentor

    Sorry, overlooked. NO NEED TO USE CAPS.
    An example isn't a proof. If you eliminate choices, you have to prove that it can be done without restricting the general case.
     
  6. Mar 11, 2017 #5

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Actually the question does say "Which of the following is TRUE for all convex sets S and T?". I would suggest that you jump straight to trying to prove E... Might save you some time over looking at lots of a examples.
     
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