Recent content by almostsure

Let $X$ be a compact and convex subset of $\mathbb{R^2}$ Let $a^1, a^2 \in X$ such that $a^j = (a^j_1, a^j_2)$, $j=1,2$ Is $c= \sum_{i=1}^2 \mathbb{I}_{ i=j} a^j_i \in X \quad ?$