Question

Let $S_1 = {(x, y) ∈ R^2 ∶ x + y ≥ 1, x + y ≤ 2, y ≥ x^2, x, y ≥ 0}$ and $S_2 = {(x, y) ∈ R^2 ∶ x + y ≥ 1, x + y ≤ 2, y ≤ x^2, x, y ≥ 0}.$ Then, which of the following is CORRECT ?

• A. Both $S_1$ and $S_2$ are convex sets
• B. $S_1$ is a convex set but $S_2$ is not a convex set
• C. $S_1$ is a convex set but $S_2$ is not a convex set
• D. Neither $S_1$ nor $S_2$ are convex sets

Answer 1

Answer: (B)

$S_1$ is a convex set but $S_2$ is not a convex set

Answer 2

The correct answer is (B): $S_1$ is a convex set but $S_2$ is not a convex set