Q:

# When Do You Use the Union Symbol in Math?

A:

The union symbol in math, which looks like a capital U, is used when it is necessary to denote the collection of all the elements of two or more sets together. The union of sets is one of the fundamental operations in set theory.

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A set is a collection of defined or distinct objects. For instance, the numbers 1, 2 and 3 are distinct objects, but when they are combined, they form the set {1,2,3}. If this set is designated as set A, and set B is {2,3,4,5}, the union of set A and set B is set C, which is {1,2,3,4,5}. The equation of the union of set A and B is written AUB=C, or {1,2,3}U{2,3,4,5}={1,2,3,4,5}. This is expressed in words as A union B equals C,.

While the union of sets combines all the elements of both sets, the intersection of sets denotes only the elements the sets have in common. For instance, if set A is {1,2,3} and set B is {2,3,4,5}, then the intersection of sets A and B is {2,3}, as these are the only elements that appear in both sets. Intersection is written with a symbol like an upside down capital U, so if the intersection of sets A and B is set C, the equation would be written A?B=C, or {1,2,3}?{2,3,4,5}={2,3}.