Question

① Prove that the intersection of two convex sets is also
convex set.
​

Answer 1

Proof-

Now, Let A and B be convex sets.(given in

To show that $(A ∩ B)$ is also convex.

Let points, $p1, p2 ∈ (A ∩ B).$

Let point “p” lie on the line segment between these two points p1 and p2.

Then p ∈ A, because A is convex, and similarly, p ∈ B because B also is convex.

Therefore, $p ∈ (A ∩ B)$

However, if the intersection set is null, a null set is also trivially Convex.

Hence proved.

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