how to prove a set is not convex

themathman

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Sep 8, 2019
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x = [1,2] U[3,4] CR

how would i go about proving this set is not convex
 

pka

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x = [1,2] U[3,4] CR how would i go about proving this set is not convex
Your notation is very poor. Lets see if this is correct.
\(\displaystyle \mathcal{X}=[1,2]\cup[3,4]\subset\mathbb{R}^1\).
If that is correct, you want to prove that \(\displaystyle \mathcal{X}\) is not convex.
So suppose that \(\displaystyle P\in [1,2] ~\&~Q\in [3,4]\) can you prove that \(\displaystyle (\exists T)[P-T-Q~\&~T\notin\mathcal{X}]\)
 
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Subhotosh Khan

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x = [1,2] U[3,4] CR

how would i go about proving this set is not convex
Please follow the rules of posting in this forum - enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/

Please share your work/thoughts with us - so that we know where to begin to help you. Also include the context - topic being taught in class now.

Please post the EXACT problem as it was presented to you.

To start with: What is/are the property/s of a convex set?
 

Dr.Peterson

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x = [1,2] U[3,4] CR

how would i go about proving this set is not convex
I would start with the definition you were given for a convex set. (This may vary according to what subject you are studying, which is one reason we ask you to state the context and show your work.)

So, please state that definition, and tell us how you see it applying to this question.
 
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