Chapter 3.8, Problem 16PPE

To determine

To Find: $A\cap B$

Answer to Problem 16PPE

The intersection of set $A=\left\{1,3,4\right\}\&B=\left\{x|x\text{ is an even number less than 9}\right\}\text{ i}\text{.e}\text{. }B=\left\{2,4,6,8\right\}$ is $A\cap B=\left\{4\right\}$

Explanation of Solution

Given information:

The sets

  $\begin{array}{l}A=\left\{1,3,4\right\},B=\left\{x|x\text{ is an even number less than 9}\right\},C=\left\{2,5,7,10\right\}\\ \&D=\left\{x|x\text{ is an odd number less than 10}\right\}\end{array}$

Concept and Formula Used:

Union of set: The union of two or more set contain all the elements of the set present in either of the set taking common elements only once.

Intersection of sets: The intersection of two or more sets is a set contain common element of all the sets.

Calculation:

The given sets are $A=\left\{1,3,4\right\}\&B=\left\{x|x\text{ is an even number less than 9}\right\}\text{ i}\text{.e}\text{. }B=\left\{2,4,6,8\right\}$

The intersection of the set is

  $\begin{array}{l}A\cap B=\left\{1,3,4\right\}\cap \left\{2,4,6,8\right\}\\ \text{Common elements of two sets :4}\\ A\cap B=\left\{4\right\}\end{array}$

Conclusion:

The intersection of set $A=\left\{1,3,4\right\}\&B=\left\{x|x\text{ is an even number less than 9}\right\}\text{ i}\text{.e}\text{. }B=\left\{2,4,6,8\right\}$ is $A\cap B=\left\{4\right\}$