if A and B are connected sets but not seperated then prove that union of A and B is connected?

Question

it is about set topology

Answer 1

From Wolfram Mathworld (see source): "A space D is connected if any two points in D can be connected by a curve lying wholly within D."

Start with two points r and s such that r, s and p are not colinear. (you'll have to show that such points exist). Show that for any point b in B you can form a line segment from either b to r or b to s such that one or the other doesn't pass through p. Since all points can be connected to either r or s and r can be connected to s, you can form a curve (consisting of 2 or 3 line segments) that connects any two points in B.

That should get you started!