Question

Closure property is applicable to ........ operation of whole numbers.

• A. inverse
• B. division
• C. subtraction
• D. addition

Answer 1

The correct option is D addition

A) The closure property of the inverse tells that the result of the inverse of the whole number is not always a whole number. Whole numbers are not closed under inverse i.e., the inverse of a = 1 ÷ a is not always a whole number. From the property, we have, 1 ÷ 2 = 0.5 (not a whole number)

B) The closure property of the division tells that the result of the division of two whole numbers is not always a whole number. Whole numbers are not closed under division i.e., a ÷ b is not always a whole number. From the property, we have, 14 ÷ 7 = 2 (whole number) but 7 ÷ 14 = ½ (not a whole number).

C) When one whole number is subtracted from another, the difference is not always a whole number. This means that the whole numbers are not closed under subtraction. If a and b are two whole numbers and a − b = c, then c is not always a whole number. Take a = 7 and b = 5, a − b = 7 − 5 = 2 and b − a = 5 − 7 = −2 (not a whole number).

D) Two whole numbers add up to give another whole number. This is the closure property of the whole numbers. It means that the whole numbers are closed under addition. If a and b are two whole numbers and a + b = c, then c is also a whole number. 3 + 4 = 7 (whole number).

Hence option $D$ is correct.