A statement for convex sets The following statement is true or false?
Given a convex set $S$ then for any $y \in S$ and $\theta\in[0,1], \theta \in \mathbb R$ there exist $y_1,y_2 \in S, y_1 \ne y, y_2 \ne y$ such that $y=\theta y_1+(1-\theta) y_2.$

You don't even need $S$ convex: just take $y_1 = y_2 = y$.
