We know that a set is convex if the straight line joining any two points of the set lies completely in the set. Or, mathematically, a set $X$ is convex if
$$x_1, x_2 \in X, 0 \leq \lambda \leq 1 \Longrightarrow\lambda x_1+(1-\lambda)x_2 \in X$$
But how do we define a concave set? Can you give an example?