Which of the following subsets of $\Bbb R$ are convex.

1) $\{(x,y) : \mid x\mid \le 5, \mid y \mid \le 10\}$,

2) $\{(x,y):x^2 + y^2 = 1\}$,

3)$\{(x,y) : y \ge x^2\}$,

4) $\{(x,y) : y \le x^2\}$.

**Solution**:

A subset $A$ of $\Bbb R^2$ is said to be convex if the line segment joining any two points of $A$ lies

**entirely**in $A$. The given sets are**option 1**:

**option 2**

option 3

option 4

From the images (shaded regions), we see that the sets which are given in

**option (1) and (3) are convex**.**here**for more problems.

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