Question

prove that the intersection of two convex is again a convex set​

Answer 1

Answer:

Theorem: Given any collection of convex sets (finite, countable or uncountable), their intersection is itself a convex set.

Proof: If the intersection is empty, or consists of a single point, the theorem is true by definition.

Otherwise, take any two points A, B in the intersection. The line AB joining these points must also lie wholly within each set in the collection, hence must lie wholly within their intersection.... hope this will help you....

Answer 2

Answer:

Theorem: Given any collection of convex sets(finite, countable or uncountable), theirintersection is itself a convex set. Proof: If theintersection is empty, or consists of a single point, the theorem is true by definition. Otherwise, take any two points A, B in theintersection.