Question

write down the properties of subtraction operation
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Answer 1

Explanation:

Closure Property - x – y ∈ Z

Associative Property - (x – y) – z ≠ x – (y – z)

Commutative Property - x – y ≠ y – x

Distributive Property - x × (y + z) = x × y + x × z

x × (y − z) = x × y − x × z

Identity Property - x – 0 = x ≠ 0 – x

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Answer 2

Answer:

This means that the whole numbers are not closed under subtraction.

Closure Property

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).

Commutative Property

Subtraction of two whole numbers is not commutative. This means we cannot subtract two whole numbers in any order and get the same result. Let a and b be two whole numbers, then a − b ≠ b − a. Take a = 7 and b = 5, 7 − 5 = 2 ≠ 5 − 7 = −2.

Associative Property

An associative property does not hold for the subtraction of whole numbers. This means that we cannot group any two whole numbers and subtract them first. Order of subtraction is an important factor. If ‘a’, ‘b’, and ‘c’ are the three whole numbers then, a − (b − c) ≠ (a − b) − c. Consider the case when a = 8, b = 5 and c = 2, 8 − (5 − 2) = 5 ≠ (8 − 5) − 2 = 1.

Subtractive Property of Zero

When we subtract zero from a whole number, the value of the whole number remains the same. Take an example, a = 98, a − 0 = 98 − 0 = 98.

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