Set Theory - Trivium Test Prep Online Courses

# Set Theory

## Set Theory

A set is any collection of items. In mathematics, a set is represented using a capital letter and curly brackets. For example, if S is the set of all integers less than 10, then S = {x|x is an integer and x < 10}. (The vertical bar | is read “such that.”)

The set that contains no elements is called the empty set or the null set and is denoted by empty brackets { } or the symbol .

The union of two sets, denoted A B, contains all the data that is in either set A or set B or both sets. The intersection of two sets, denoted AB, includes only elements that are in both A and B.

A = {1, 4, 7} and B = {2, 4, 5, 8}

A B = {1,2,4,5,7,8}

AB = {4}

Unions and intersections can be understood in terms of a Venn diagram. The Venn diagram below shows two sets, A and B. The union of A and B is the entire area of the diagram; the intersection of sets A and B is the shaded area where they overlap.

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