Question

Which of the following statements is/are incorrect?
(i) Whole numbers are closed under subtraction.
(ii) Integers are not closed under division.
(iii) Rational numbers are closed under division.
(Hint: A set of numbers is said to be closed under an operation if the result of the operation between the operands belongs to the same set.)

• A. Only (i)
• B. Only (ii)
• C. Both (i) and (ii)
• D. Both (i) and (iii)

Answer 1

The correct option is D Both (i) and (iii)

Let’s analyze the options using examples.

(i) $5-9=-4$, which is not a whole number but 5 and 9 are whole numbers. So, whole numbers are not closed under subtraction.

(ii) $(-6)÷7=0.857$, which is not an integer but -6 and 7 are integers. So integers are not closed under division.

(iii) $\frac{4}{3}÷0$ is not defined but $\frac{4}{3}$ and 0 are rational numbers. So, rational numbers are not closed under division

Hence, statements (i) and (iii) are incorrect.