# how to prove a set is not convex

#### themathman

##### New member
x = [1,2] U[3,4] CR

how would i go about proving this set is not convex

#### pka

##### Elite Member
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 $$\displaystyle (\exists T)[P-T-Q~\&~T\notin\mathcal{X}]$$

Last edited:

#### Subhotosh Khan

##### Super Moderator
Staff member
x = [1,2] U[3,4] CR

how would i go about proving this set is not convex
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