Question

Rational numbers are closed under addition and multiplication but not under subtraction.

• A. True
• B. False

Answer 1

The correct option is B False

According to the properties of rational numbers: Rational numbers are closed under addition, subtraction, and multiplication.

Closure Property

Assume two rational numbers say $x$ and $y$ the results of addition, subtraction and multiplication operations give a rational number. We can say that rational numbers are closed under addition, subtraction and multiplication. For example:

• $\frac{1}{2}+\frac{3}{4}=\frac{5}{4}$
• $\frac{3}{4}-\frac{1}{2}=\frac{1}{4}$
• $\frac{2}{3}\times \frac{3}{4}=\frac{1}{2}$

The division is not under closure property because division by zero is not defined. We can also say that except $‘0’$ all numbers are closed under division.

Hence, the given statement is False.