Question

Which of the following sets are convex?

Options

• {(x, y) : x² + y² ≥ 1}

•  {(x, y) : y² ≥ x}

•  {(x, y) : 3x² + 4y² ≥ 5}

•  {(x, y) : y ≥ 2, y ≤ 4}

   

Answer 1

{(x, y) : y ≥ 2, y ≤ 4}

{(x, y) : y ≥ 2, y ≤ 4} is the region between two parallel lines, so any line segment joining any two points in it lies in it. Hence, it is a convex set.