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Show that A union B is not a convex set?
In some cases, A union B is convex, but in general this may not be true. Consider two sets A, B (subsets of Rn) such that A intersect B is the null set. Now choose a point x in A, and y in B. If a set is to be convex, then all points on the line tx + (1-t)y (0
Intersection of two convex set is convex?
The proof of this theorem is by contradiction. Suppose for convex sets S and T there are elements a and b such that a and b both belong to S∩T, i.e., a belongs to S and T and b belongs to S and T and there is a point c on the straight line between a and b that does not belong to S∩T. This would mean that c does not belong to one of the sets S or T or both. For whichever set c does not belong to this is a contradiction of that set's convexity, contrary to assumption. Thus no such c and a and b can exist and hence S∩T is convex.
How will you write using the venn diagram the union of set a(1234) and the intersection of set b(10111213) and set c(1213)?
If B = {10111213} and C = {1213} then their intersection is the empty set, {}.The union of A with an empty set is set A.
What do you call a set of elements which belong to A or to B or to both?
The union of A and B.
Is there any case when union and intersection are same in sets?
if we have set A and B consider A={1,2,3,4}and B={3,4,5,6} the union of these sets is A and B={1,2,3,4,5,6}and the intersection is{3,4} the union and the intersection are same only if A=B
