Prove that certain sets are not convex. For each of the following sets, give the coordinates of two points where P and Q are in the set, but the line from P to Q goes outside the set.

(a) R = {(x , y ): x ² + y ² ≥ 1, y<0}

(b) S = {(x , y ): (x - 1) ² + y ² ≤ 1} ∪ {(x , y ): (x + 1) ² + y ² ≤ 1}

(c) T = {(x , y ): x ² >2} ∩ {(x , y ): y ² <4}

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a R x y x 2 y 2 1 y 0 Not convex P 32 12 P ... View the full answer