Which of the following sets are convex? - Vidyadip

MCQ

Which of the following sets are convex?

A
$\{(\text{x},\text{y}):\text{x}^2+\text{y}^2\geq1\}$
B
$\{(\text{x},\text{y}):\text{y}^2\geq\text{x}\}$
C
$\{(\text{x},\text{y}):3\text{x}^2+4\text{y}^2\geq5\}$
✓
$\{(\text{x},\text{y}):\text{y}\geq2,\text{y}\leq4\}$

✓

Answer

Correct option: D.

$\{(\text{x},\text{y}):\text{y}\geq2,\text{y}\leq4\}$

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.

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