Chapter 4.3, Problem 3E

a.

To determine

To state: Whether the given statement is true or false.

Answer to Problem 3E

The statement is true.

Explanation of Solution

Given:

The following expression:

  $2\cancel{|}5$

The given expression can be written in words as:

Two does not divide five.

The above sentence is true as $5$ is not a multiple of $2$ . Hence when $5$ is divided by $2$ , it leaves a remainder.

  $2\begin{array}{c}\hfill 2\\ \hfill \overline{)\begin{array}{l}5\\ \underset{\_}{4}\\ 1\end{array}}\end{array}$

b.

To determine

To state: Whether the given statement is true or false.

Answer to Problem 3E

The statement is true.

Explanation of Solution

Given:

The following expression:

  $n\cancel{|}\left(n+1\right)\text{ if }n\ge 2$

Let n be $2$ . Therefore $n+1=2+1=3$

The above sentence is true as $3$ is not a multiple of $2$ . Hence when $3$ is divided by $2$ , it leaves a remainder.

  $2\begin{array}{c}\hfill 1\\ \hfill \overline{)\begin{array}{l}3\\ \underset{\_}{2}\\ 1\end{array}}\end{array}$

c.

To determine

To state: Whether the given statement is true or false.

Answer to Problem 3E

The sentence is false.

Explanation of Solution

Given:

The following expression:

  $5\cancel{|}0$

The given expression can be written in words as:

Five does not divide zero.

The above sentence is false as $0$ is a multiple of $5$ . Hence when $0$ is divided by $5$ , it does not leave a remainder.

  $5\begin{array}{c}\hfill 0\\ \hfill \overline{)\begin{array}{l}0\\ \underset{\_}{0}\\ 0\end{array}}\end{array}$