Chapter 2.CR, Problem 1CR

To determine

a. To find:

$A\cup B$

Answer to Problem 1CR

Solution:

$A\cup B=\left\{1,2,3,4,5,6,7,9,10\right\}$.

Explanation of Solution

Given,

$A\cup B$

Let,

$U=\left\{1,2,3,4,5,6,7,8,9,10\right\}$

$A=\left\{1,3,5,7,9\right\}$

$B=\left\{2,4,6,9,10\right\}$

The union is set consisting of all elements of A or B or both.

$A\cup B=\left\{1,2,3,4,5,6,7,9,10\right\}$

Thus, $A\cup B=\left\{1,2,3,4,5,6,7,9,10\right\}$

Final statement:

Therefore, $A\cup B=\left\{1,2,3,4,5,6,7,9,10\right\}$.

To determine

b. To find:

$A\cap B$

Answer to Problem 1CR

Solution:

$A\cap B=\left\{9\right\}$.

Explanation of Solution

Given,

$A\cap B$

Let,

$U=\left\{1,2,3,4,5,6,7,8,9,10\right\}$

$A=\left\{1,3,5,7,9\right\}$

$B=\left\{2,4,6,9,10\right\}$

The intersection is set consisting of all elements common to A and B.

$A\cap B=\left\{9\right\}$

Thus, $A\cap B=\left\{9\right\}$.

Final statement:

Therefore, $A\cap B=\left\{9\right\}$.

To determine

c. To find:

$\overline{A}$

Answer to Problem 1CR

Solution:

$\overline{A}=\left\{2,4,6,8,10\right\}$.

Explanation of Solution

Given,

$\overline{A}$

Let,

$U=\left\{1,2,3,4,5,6,7,8,9,10\right\}$

$A=\left\{1,3,5,7,9\right\}$

$B=\left\{2,4,6,9,10\right\}$

The set that contained in U, but not contained in A is known as complement of A.

$\overline{A}=\left\{2,4,6,8,10\right\}$

Thus, $\overline{A}=\left\{2,4,6,8,10\right\}$

Final statement:

Therefore, $\overline{A}=\left\{2,4,6,8,10\right\}$

To determine

d. To find:

$\overline{B}$

Answer to Problem 1CR

Solution:

$\overline{B}=\left\{1,3,5,7,8\right\}$.

Explanation of Solution

Given,

$\overline{B}$

Let,

$U=\left\{1,2,3,4,5,6,7,8,9,10\right\}$

$A=\left\{1,3,5,7,9\right\}$

$B=\left\{2,4,6,9,10\right\}$

The set that contained in U, but not contained in B is known as complement of B.

$\overline{B}=\left\{1,3,5,7,8\right\}$

Thus, $\overline{B}=\left\{1,3,5,7,8\right\}$

Final statement:

Therefore, $\overline{B}=\left\{1,3,5,7,8\right\}.$