Chapter 7, Problem 1CRE

(a)

To determine

To find $A\cup B$ for the given sets A and B.

Answer to Problem 1CRE

Solution:

  $A\cup B=\left\{2,4,6,8,10,12,16\right\}$ .

Explanation of Solution

Given:

  $A=\left\{2,4,6,8,10\right\}$ & $B=\left\{2,8,12,16\right\}$

Concept Used:

The union of two set A and B is the set of elements which are in A, B or in both.

Calculation:

We have been given two sets $A=\left\{2,4,6,8,10\right\}$ and $B=\left\{2,8,12,16\right\}$ . In order to find union of these two sets, we’ll use the above-mentioned definition. The elements $\left\{2,8\right\}\in A,B\left(\text{Elements which are common in A and B}\right)$

  $\left\{4,6,10\right\}\in A\left(\text{Elements which are in A but not in B}\right)$

  $\left\{12,16\right\}\in B\left(\text{Elements which are in B but not in A}\right)$

  $A\cup B=\left\{2,4,6,8,10,12,16\right\}\left(\text{By the above definition}\right)$ .

Conclusion:

  $A\cup B=\left\{2,4,6,8,10,12,16\right\}$

(b)

To determine

To find:The intersection of given sets.

Answer to Problem 1CRE

Solution:

The intersection of the given sets is $A\cap B=\left\{2,8\right\}$ .

Explanation of Solution

Given:

  $A=\left\{2,4,6,8,10\right\}$ & $B=\left\{2,8,12,16\right\}$

Concept Used:

The intersection of two set A and B is the set of elements which are in both A and B.

Calculation:

We have been given two sets $A=\left\{2,4,6,8,10\right\}$ and $B=\left\{2,8,12,16\right\}$ . In order to find intersection of these two sets, we’ll use the above mentioned definition. The elements $\left\{2,8\right\}\in A,B\left(\text{Elements which are common in A and B}\right)$

  $\left\{4,6,10\right\}\in A\left(\text{Elements which are in A but not in B}\right)$

  $\left\{12,16\right\}\in B\left(\text{Elements which are in B but not in A}\right)$

  $A\cap B=\left\{2,8\right\}\left(\text{By the above definition}\right)$ .

Conclusion:

  $A\cap B=\left\{2,8\right\}$