Q77.. - Algebra 2

Question

Use the following information.

The product of any two whole numbers is always a whole number. So, the set of whole number is said to be closed under multiplication. This is an example of the Closure Property.

State whether each statement is true or false. If false, given a counterexample.

77. The set of whole numbers is closed under division. 

Step-by-Step Solution

Answer

Given statement is false. Counterexample is, divide whole numbers 1 by 2 gives $\frac{1}{2}$ which is not a whole number.

Step 1 - Define whole numbers

The set $\left\{0,1,2,3,4,5,...\right\}$ is called the set of whole number.

Step 2 - Divide any two whole numbers

Let a and b be any two whole number.

Let D be the division of these two integers

$D=\frac{a}{b}$

Step 3 - Check statement is true or false

As division of two whole numbers may or may not give whole number so set of whole number is not closed under division. 

One counter example is

Substitute 1 for a and 2 for b then 

$D=\frac{1}{2}$