Q74. - 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.

The set of integers is closed under multiplication. 

Step-by-Step Solution

Answer

Given statement is true. 

Step 1 - Define integers

The set $\left\{...,-3,-2,-1,0,1,2,3,...\right\}$ is called the set of integer number.

Step 2 - Multiply any two integers

Let a  and b be any two integers.

Let M be the multiplication of these two integers

M=ab 

Step 3 - Check statement is true or false

As product of two integers is always an integer so set of integers is closed under multiplication.