Chapter 3.8, Problem 2P

a.

To determine

The intersection of set $A=\{2,4,6,8\}$ and $B=\{0,2,5,7,8\}$ .

Answer to Problem 2P

  $A\cap B=\{2,8\}$

Explanation of Solution

Given information :

Given two sets, $A=\{2,4,6,8\}$ and $B=\{0,2,5,7,8\}$ .

To find the intersection of two sets, we will write the elements that are common in both the sets.

  $\begin{array}{l}A=\{2,4,6,8\}\\ B=\{0,2,5,7,8\}\end{array}$

So, intersection of A & B:

  $A\cap B=\{2,8\}$

b.

To determine

The intersection of set $A=\{2,4,6,8\}$ and $C=\{n|n\text{ is }anoddwholenumber\}$ .

Answer to Problem 2P

  $A\cap C=\left\{\right\}or\varphi$

Explanation of Solution

Given information :

Given two sets, $A=\{2,4,6,8\}$ and $C=\{n|n\text{ is }anoddwholenumber\}$ .

To find the intersection of two sets, we will write the elements that are common in both the sets.

  $\begin{array}{l}A=\{2,4,6,8\}\\ C=\{n|n\text{ is }anoddwholenumber\}\end{array}$

Write the set C using elements.

Odd whole numbers are: 1, 3, 5, 7, 9, 11,…

  $C=\{1,3,5,7,9,11,\mathrm{...}\}$

Here no common elements in both the sets.

So, intersection of A & C:

  $A\cap C=\left\{\right\}or\varphi$

c.

To determine

The intersection of set $B=\{0,2,5,7,8\}$ and $C=\{n|n\text{ is }anoddwholenumber\}$ .

Answer to Problem 2P

  $C\cap B=\left\{7\right\}$

Explanation of Solution

Given information :

Given two sets, $B=\{0,2,5,7,8\}$ and $C=\{n|n\text{ is }anoddwholenumber\}$ .

To find the intersection of two sets, we will write the elements that are common in both the sets.

  $\begin{array}{l}C=\{n|n\text{ is }anoddwholenumber\}\\ B=\{0,2,5,7,8\}\end{array}$

Write the set C using elements.

Odd whole numbers are: 1, 3, 5, 7, 9, 11,…

  $C=\{1,3,5,7,9,11,\mathrm{...}\}$

So, intersection of C & B:

  $C\cap B=\left\{7\right\}$