College Math

College Math Study Guide

An empty set is a set which has no elements, and is denoted by { } = ø. Further, two sets, A and B, are equal if all the elements in those sets are equal and same, and we denote them as A = B. If the both sets are not equal, then we write them as A≠ B. The number of elements in a set A is denoted by n(A). Further, the subset of a set is denoted by the following symbol: B ⊆ A It means that B is a sub- set of A, that is, all the elements of set B are present in the set A. Also, remember that whenever we have a set that have N number of elements, then the total number of sub- sets for that set would be 2 N . For instance, suppose we have a set A, such that A = {1, 2, 3}, then the total number of sub- set of A would be 2 3 that is 8. That are, { }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3} and {1, 2, 3} 6.12 Operations on Sets We can have different operations on sets, and generally consists of union of sets, intersection of sets and complement of sets. Let us understand them one by one, using illustrations and Venn diagrams. Union of S ts: Suppose we are given two subsets, A and B, then the union of A and B implies all those elements which are present in set A, set B or both A and B. It is denoted by the symbol ∪. For instance, we are given the following sets: A = {2, 4, 6, 8} and B = {1, 2, 3, 4, 5} Then A ∪ B = {1, 2, 3, 4, 5, 6, 8} We can represent the sets and their operations using Venn diagrams. The union of two sets is given by the Venn diagram as demonstrated here:

©2018

Achieve

Page 108

of 120