I will prove a more general theorem from which your answer follows immediately. Theorem: The intersection of any number (including 2) of convex polygons is convex.
Proof
Let C be the intersection of Ci which is a set of iconvex polygons. By definition of intersection, if two points A and B belong to C then they belong to every one of the Ci . But the convexity of each of the Ci tells us that line segment AB is contained in Ci . Therefore, the line segment AB is in C and because ABwas arbitrary we conclude that C is convex
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Both union and intersection are commutative, as well as associative.
Well, depending on how you want it, either a convex, reflex, or regularhendecagon , or a eleven-gon. I think this is how they look like though.
A set is a collection of well defined objects known as elements Opperatons of sets are 1)union - the union of sets A and B is the set that contains all elements in A and all elements in B. intersection - given two sets A and B, the intersection of A and B is a set that contains all elements in common between A and B. compliments - given set A, A compliment is the set of all elements in the universal set but not in A difference - A-B is a set containing all elements in A that are not in B. symmetric difference - it is the sum of A and B minus A intersection B.
You can prove a fact is true by looking it up on several Internet sites or a book. When looking up a fact make sure that the source you are using is reputable and well versed in the subject you are looking for. It is also a good idea to cross-reference the fact on several sites.
The set is well defined. Whether or not a given integer belongs to the set of prime numbers is clearly defined even if, for extremely large numbers, it may prove impossible to determine the status of that number.