Chapter 1, Problem 24MCQ

To determine

Todescribe:The given statement is true or false.

Answer to Problem 24MCQ

The given statement is true.

Explanation of Solution

Given information:

Statement: The difference of two whole number is always a whole number.

Methodused:

Definition of whole number: A number of the form $N=z\pm \alpha$ where z is an integer and $\alpha$ is number greater than 0 and less than 1 is called a fractional number. When $\alpha =0$ , the number $N=z$ is a whole number.

Suppose $N_1=z_1\pm {\alpha }_1$ and $N_2=z_2\pm {\alpha }_2$ be any two numbers, fractional or whole numbers.

Then $N_1+N_2=\left(z_1\pm {\alpha }_1\right)+\left(z_2\pm {\alpha }_2\right)$

$\Rightarrow N_1+N_2=\left(z_1+z_2\right)\pm \left({\alpha }_1+{\alpha }_2\right)$   .... (1)

Now let $N_1$ and $N_2$ are two whole numbers.

  $\Rightarrow {\alpha }_1=0,{\alpha }_2=0$

  $\Rightarrow N_1+N_2=\left(z_1+z_2\right)\pm \left(0+0\right)$

  $\Rightarrow N_1+N_2=\left(z_1+z_2\right)\pm 0$

  $\Rightarrow N_1+N_2=\left(z_1+z_2\right)$ = an integer that a whole number.

Thus, the sum of two whole numbers is always a whole number.

Hence, the given statement is true.

Conclusion:

The given statement is true.