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# Intersection of Sets

Top
 Sub Topics In set theory, intersection of sets is one of the important operations. The term intersection tells us it is a collection of common elements. We can perform this operation on two or more than two sets. The common outcomes in all sets falls in a separate and single set which is called intersection of sets. We can say that when two sets intersects each other or contains common elements then this part or the collection of these elements is called intersection of sets. Intersection is denoted by $\cap$. If we have two events A and B then A $\cap$ B is called intersection of A and B. For Example: A = {2, 5, 6} and B = {15, 2, 10} then A $\cap$ B = {2}.

## Definition

Intersection of events is the intersection of two or more than two events. We can say that when two sets contain common elements then the collection of these elements is called intersection. All those elements of given sets or events which are common form a new event which is called intersection of events.
Intersection is denoted by $\cap$. If we have two events A and B then A $\cap$ B is called intersection of A and B.

## How to Calculate

The calculation of intersection of events is easy to understand. If we have two sets of event and we are asked to find the intersection of events then we just collect all common elements of both given sets and put these in a new set and this new formed set is called intersection of given events.

Like We have two sets of events P={2, 4, 6, 8, 10, 12} and Q={4, 8, 12, 16}. If we need to find the intersection of P and Q.
Then we collect common elements in P and Q. So, the intersection of P and Q is:
P $\cap$ Q= {4, 8, 12}

## Examples

Example 1: If A={x, y, z, a, b} B={x, y, z, 0} then find out intersection of A and B.

Solution: The given events are

A={x, y, z, a, b} B={x, y, z, 0}

Since, the common elements in A and B are x, y and z. So
A $\cap$  B ={x, y, z}

Example 2: If P = {2, 4, 6, 8} and Q = {1, 5, 9} and R = {a, b, c} then find out intersection of P, Q and R.

Solution:  The given events are:

P = {2, 4, 6, 8} and Q = {1, 5, 9} and R = {a, b, c}

Since, there is not any element common in all three events P, Q and R. So

P $\cap$ Q $\cap$ R = { } or $\phi$

Example 3: If A = {All positive numbers} and B = {All even numbers} then find out A $\cap$ B.

Solution:   Given events:

A = {All positive numbers} and B = {All even numbers}

Since, all positive numbers contains all even numbers also. It means all even numbers are common in both A and B sets. So, A $\cap$ B = {All even numbers}