Chapter 3.8, Problem 14PPE

To determine

To Find: $B\cup D$

Answer to Problem 14PPE

The union of set

  $\begin{array}{l}B=\left\{x|x\text{ is an even number less than 9}\right\}\text{ i}\text{.e}\text{. }B=\left\{2,4,6,8\right\}\\ D=\left\{x|x\text{ is an odd number less than 10}\right\}\text{ i}\text{.e}\text{. }D=\left\{1,3,5,7\right\}\end{array}$

is $B\cup D=\left\{1,2,3,4,5,6,7,8\right\}$

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

  $\begin{array}{l}B=\left\{x|x\text{ is an even number less than 9}\right\}\text{ i}\text{.e}\text{. }B=\left\{2,4,6,8\right\}\\ D=\left\{x|x\text{ is an odd number less than 10}\right\}\text{ i}\text{.e}\text{. }D=\left\{1,3,5,7\right\}\end{array}$

The union of the set is

  $\begin{array}{l}B\cup D=\left\{2,4,6,8\right\}\cup \left\{1,3,5,7\right\}\\ B\cup D=\left\{1,2,3,4,5,6,7,8\right\}\end{array}$

Conclusion:

The union of set

  $\begin{array}{l}B=\left\{x|x\text{ is an even number less than 9}\right\}\text{ i}\text{.e}\text{. }B=\left\{2,4,6,8\right\}\\ D=\left\{x|x\text{ is an odd number less than 10}\right\}\text{ i}\text{.e}\text{. }D=\left\{1,3,5,7\right\}\end{array}$

is $B\cup D=\left\{1,2,3,4,5,6,7,8\right\}$