Question

The closure property on integers holds for subtraction and not for division. What about rational numbers? Verify.

Answer 1

Let 0 and 1/2 be two rational numbers 0 – 1/2 = 1/2 is a rational number

∴ Closure property for subtraction holds for rational numbers.

But consider the two rational number 5/2 and 0.

5/2 ÷ 0 = 5/(2 × 0) = 5/0

Here denominator = 0 and it is not a rational number.

∴ Closure property is not true for division of rational numbers.