Question: a. Prove that the intersection of two convex sets is a convex set. b. Show by example that the union of two convex sets may

a. Prove that the intersection of two convex sets is a convex set.

b. Show by example that the union of two convex sets may not be a convex set.

c. Give an example of two disjoint convex sets whose union is a convex set.

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