Question

Which of the following properties are not applicable to the subtraction of whole numbers?

A

Closure property

B

Commutative property

C

Associative proptery

D

All the above

Medium

Solution

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Correct option is D)

Let us have a look at the properties of whole numbers under subtraction:

(i)Β Closure property :Β If and are two whole numbers such that or , then is a whole number. If , then subtraction is not possible in whole numbers. For example: If and then,

which is not a whole number.

Therefore,Β whole numbers are not closed underΒ subtraction.

(ii)Β Commutative property :Β The subtraction of whole numbers is not commutative, that is, if and are two whole numbers, then in general is not equal to .

Verification:

We know that but which is not a whole number. Thus, for two whole numbers and if , then is a whole number but is not possible and if , then is a whole number but is not possible.

Therefore,Β whole numbers are not commutative underΒ subtraction.

(iii)Β Associative of addition :Β The subtraction of whole numbers is not associative. That is, if are three whole numbers, then in general is not equal to .

Verification:

We have,

,

and,

So, .

Therefore,Β whole numbers are not associativeΒ underΒ subtraction.

Hence, all of the properties are not applicable toΒ subtractionΒ of whole numbers.

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