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Which of the ...

Question

Which of the following sets are convex?
(a) {(x, y) : x² + y²≥ 1}
(b) {(x, y) : y² ≥ x}
(c) {(x, y) : 3x² + 4y² ≥ 5}
(d) {(x, y) : y ≥ 2, y ≤ 4}

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Solution

(d) {(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.

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