Which of the following properties are not applicable to the subtraction of whole numbers?
All the above
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Correct option is D)
Let us have a look at the properties of whole numbers under subtraction:
(i) Closure property : If a and b are two whole numbers such that a>b or a=b, then a–b is a whole number. If a<b, then subtraction a–b is not possible in whole numbers. For example: If a=3 and b=5 then,
3−5=−2 which is not a whole number.
Therefore, whole numbers are not closed under subtraction.
(ii) Commutative property : The subtraction of whole numbers is not commutative, that is, if a and b are two whole numbers, then in general a–b is not equal to (b–a).
We know that 9–5=4 but 5–9=−4 which is not a whole number. Thus, for two whole numbers a and b if a>b, then a–b is a whole number but b–a is not possible and if b>a, then b–a is a whole number but a–b is not possible.
Therefore, whole numbers are not commutative under subtraction.
(iii) Associative of addition : The subtraction of whole numbers is not associative. That is, if a,b,c are three whole numbers, then in general a–(b–c) is not equal to (a–b)–c.
Therefore, whole numbers are not associative under subtraction.
Hence, all of the properties are not applicable to subtraction of whole numbers.