Question

what are the operations are satisfied under closure property in a set of whole numbers ?​

Answer 1

Answer:

As division with zero is not possible. Hence, closure property is satisfied in whole numbers

Answer 2

Closure Property

Addition

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).

Subtraction

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).

Multiplication

Multiplication of two whole numbers will result in a whole number. Suppose, a and b are the two whole numbers and a × b = c, then c is also a whole number. Let a = 10, b = 5, 10 × 5 = 50 (whole number). The whole number is closed under multiplication.

Division

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).

Therefore,

• Addition and Multiplication are closed under whole numbers.
• Subtraction and Division aren't closed under whole numbers.

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