Question

Which of the following set is convex.
A. The set $\{(x_1, x_2) \mid \frac{x_1^2}{4} + \frac{x_2^2}{9} \le 1, x_1 \ge 0, x_2 \ge 0\}$ B. The set $\{(x_1, x_2) \mid x_1 x_2 \ge 1, x_1 \ge 0, x_2 \ge 0\}$ C. The set $\{(x_1, x_2) \mid x_1 \ge 1 \text{ or } x_2 \ge 1\}$ D. The set $\{(x_1, x_2) \mid x_1 + x_2 \le 1, x_1 \ge 0, x_2 \ge 0\}$ Choose the correct answer from the options given below:

• A. A, B, C Only
• B. A, B, D Only
• C. B, C, D Only
• D. A, D Only

Hint:

Sets defined with "OR" conditions (like $x_1 \ge 1 \text{ or } x_2 \ge 1$) correspond to unions of sets and are generally NOT convex!

Answer 1

The Correct Option is B