# Intersection of sets, definition, | examples

By | October 5, 2022

When a set of objects belong to one particular and at the same time belongs to another set is called the intersection of the set. If members of set A also belong to members of set B is called the intersection of A and B.

## What is the Intersection of sets?

The intersection of sets simply means the group of objects or members that are common in two or more given sets. This means members or objects that two or more sets have in common. Mathematical, the symbol for the intersection of sets is “∩”. For example, if A={2,4,6,8,10,12} and B={1,2,3,4,5,6}. Then A ∩ B = {2,4,6} because they are the three members that are common in sets A and B. In the Venn diagram below the intersection of the two sets is the shaded region

## Complement of Intersection of sets

Complement sets are sets’ objects or members that are present in one set but not found in another set. Given two sets A and B, the complement of A (i.e A’) are elements that are contained in set B but are not common in set A. For example, if A={1,2,3,4,5,6,7,8,9,10,11,12,13} and B={2,4,6,8,10,12}, then the complement of B ={1,3,5,7,9,11,13}.

Complement of Intersection sets are sets of objects that are not common to the two sets in question. For example, if set A={1,2,3,4,5,6,7} and set B={2,4,6,8}, find (A ∩ B)’. To find A Intersection B complement, First, find A ∩ B ={2,4,6} and then find (A ∩ B)’ ={ 1,3,5,7,8}. i.e members that are not common in set A and set B.

Let’s look at some examples of the Intersection of sets and complement of Intersection of sets.

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1) if U is the universal set, U ={1,3,5,7,9,11,13}, A is a subset {1,3,5,7,13} and B is a subset {1,3,9,11,13}, find:

(a) A’ (b) B’ (c) A ∩ B’ (d) A’ ∩ B (e) (A ∩ B)’

Solution:

(a) A’ are members that belong to the universal set but not in A. i.e A’ ={9,11}.

(b) B’ are members that belong to the universal set but they are not in B i.e B’ ={5,7}

(c) A ∩ B’ are members that belong to both A and B’. To find A ∩ B’ first list the members of sets A and B’ and then pick their Intersection. A={1,3,5,7,13) and B’ ={5,7), ∴ A ∩ B’ ={5,7}

(d) A’ ∩ B are members that belong to A’ and also belong to B. To find A’ ∩ B, first list the members of set A’ ={9,11 } and members of set B ={1,3,9,11,13}. Therefore, A’ ∩ B = {9,11}

(e) (A ∩ B)’ are members that belong to the universal set but not in A Intersection B all complement. To find this first list the members of A ∩ B ={1,3,13}. Therefore (A ∩ B)’={5,7,9,11}.

In general, the complement of a set is equal to elements of the universal set minus elements of the set in question.