Chapter 1.4, Problem 1GP

To determine

Whether the subtraction of whole numbers is commutative or no. If not, then give a counterexample.

Answer to Problem 1GP

  $\text{No}$

Explanation of Solution

Given information:

Is the subtraction of whole numbers commutative?

Concept Used:

Commutative property:

  $a+b=b+a$

  $a\cdot b=b\cdot a$

Associative property:

  $\left(a+b\right)+c=a+\left(b+c\right)$

  $\left(a\cdot b\right)\cdot c=a\cdot \left(b\cdot c\right)$

Distributive property:

  $a\left(b+c\right)=ab+ac$

  $\left(b+c\right)a=ba+ca$

Additive identity:

  $a+0=0+a=a$

Multiplicative identity:

  $a\cdot 1=1\cdot a=a$

Zero property of Multiplication:

  $a\cdot 0=0\cdot a=0$

Calculation:

The subtraction of two whole numbers is not commutative, because the difference between the number will be same but while subtracting a smaller number from larger number, the resulting number will be positive. While subtracting a larger number from a smaller whole number will result in a negative number. So, the subtraction of whole numbers is not commutative.

For example,

  $9-3\ne 3-9$

On subtracting 3 from 9, it will give the value 6. While subtracting 9 from 3 will result in $-6$ . It implies that the subtraction of two whole numbers is not commutative.

Thus, the subtraction of whole numbers is not commutative.