Question

A: Rational numbers are always closed under division.

R: Division by zero is not defined.

• A. A is true and R is the correct explanation of A
• B. A is false and R is false
• C. A is true and R is false
• D. A is false and R is true

Answer 1

The correct option is D A is false and R is true

Statement A: False

$0$ is a rational number because it can be written as $\frac{0}{1}$. When we divide any rational number by $0$ which is also a rational number, then the resultant number is of the form $\frac{m}{0}$ where $m$ is any rational number.

So, the resultant is not defined and hence rational numbers are not closed under division

Statement R: True

Any Real number divided by $0$ is not defined.