Question

Which of the following is not a convex set?
(a) {(x, y) : 2x + 5y < 7}
(b) {(x, y) : x² + y² ≤ 4}
(c) {x :|x| = 5}
(d) {(x, y) : 3x² + 2y² ≤ 6}

Answer 1

(c) {x :|x| = 5}

|x| = 5 is not a convex set as any two points from negative and positive x-axis if are joined will not lie in set.