1. the union of two convex sets is a convex sex _______
2. The union of any two convex sets, which have at least two points in common, is a convex set. __________
need your help on this convex sets true or false.
thanks
Is the red figure convex? What about the blue one? If you can't answer the first question, you need to study the definition of a convex set and read about examples of sets that are convex and not convex. If this is the case (and note that I only want to say the following if you can't answer the first question), then it is unreasonable to believe that you can solve a problem without knowing the definition, and it would be a waste of time to involve other people in helping you to solve the problem.
I can only conclude from this that you do not know what a convex set is- which makes me wonder why you were given such a problem. A set is "convex" if and only if, given any two points in the set, every point on the line segment between the two points is also in the set. Can you use that, and the pictures emakarov shows, to answer the questions.