Chapter 1.7, Problem 44E

a.

To determine

To explain : Whether the statement is always, sometimes or never true.

Answer to Problem 44E

The statement is sometimes true.

Explanation of Solution

Given information :

If $k$ is any integer and $n$ is less than 0, then $nk$ is less than $n$ .

Since $n$ is less than 0, so $n$ will be negative and if $k$ is also negative than $nk$ will be positive which is greater than $n$ . Also,

If $k$ is positive then $nk$ will be negative and in this case $nk$ will be less than $n$ .

Hence,

The statement is sometimes true.

a.

To determine

To explain : Whether the statement is always, sometimes or never true.

Answer to Problem 44E

The statement is sometimes true.

Explanation of Solution

Given information :

If $k$ is any integer and $n$ is greater than 1, then $nk$ is greater than $n$ .

Since $n$ is greater than 1, so $n$ will be positive and if $k$ is also positive than $nk$ will be positive which is greater than $n$ . Also,

If $k$ is negative then $nk$ will be negative and in this case $nk$ will be less than $n$ .

Hence,

The statement is sometimes true.