Chapter 5.8, Problem 20P

Reasoning Examine the expressions $[m-n\mid \text{ and }|n-m|.\text{ Substitute }m=2$ and $n=3$ in each expression and simplify. Now, substitute $m=3$ and $n=2$ in each expression and simplify. Repeat this process with 3 other sets of numbers for $m$ and n. What is your conclusion?

To determine

To examine the given expression.

Answer to Problem 20P

For any pair the result will remain same for both expressions.

Explanation of Solution

Given:

Expressions:

  $|m-n|\&|n-m|$

Concept used:

A modulus function is a function which gives the absolute value of a number or variable. 

Calculation:

When, $m=2\&n=3$

Then,

  $\begin{array}{l}|m-n|\\ =|2-3|\\ =|-1|\\ =1\\ |n-m|\\ =|3-2|\\ =\left|1\right|\\ =1\end{array}$

When, $m=3\&n=2$

Then,

  $\begin{array}{l}|m-n|\\ =|3-2|\\ =\left|1\right|\\ =1\\ |n-m|\\ =|2-3|\\ =|-1|\\ =1\end{array}$

When, $m=5\&n=7$

Then,

  $\begin{array}{l}|m-n|\\ =|5-7|\\ =|-2|\\ =2\\ |n-m|\\ =|7-5|\\ =\left|2\right|\\ =2\end{array}$

When, $m=7\&n=5$

Then,

  $\begin{array}{l}|m-n|\\ =|7-5|\\ =\left|2\right|\\ =2\\ |n-m|\\ =|5-7|\\ =|-2|\\ =2\end{array}$

When, $m=4\&n=8$

Then,

  $\begin{array}{l}|m-n|\\ =|4-8|\\ =|-4|\\ =4\\ |n-m|\\ =|8-4|\\ =\left|4\right|\\ =4\end{array}$

When, $m=8\&n=4$

Then,

  $\begin{array}{l}|m-n|\\ =|8-4|\\ =\left|4\right|\\ =4\\ |n-m|\\ =|4-8|\\ =|-4|\\ =4\end{array}$

When, $m=8\&n=11$

Then,

  

When, $m=11\&n=8$

Then,

  $\begin{array}{l}|m-n|\\ =|11-8|\\ =\left|3\right|\\ =3\\ |n-m|\\ =|8-11|\\ =|-3|\\ =3\end{array}$

Conclusion:

Therefore, for any pair the result will remain same for both expressions.