Q76. - 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 rational numbers is closed under addition. 

Step-by-Step Solution

Answer

Given statement is true.

Step 1 - Define rational numbers

The set of rational number has numbers in the ratio form $\frac{m}{n}$, where m and n are integers and n is non-zero. The decimal form of a rational number is either a terminating or repeating decimal.

Step 2 - Add any two rational numbers

Let $\frac{m}{n}$ and $\frac{p}{q}$ be any two rational number.

Let A be the addition of these two integers

$A=\frac{m}{n}+\frac{p}{q}$

Step 3 - Check statement is true or false

As additional of two rational number is always a rational number so it is closed under addition.