prepare the table chart of properties of natural number,whole number,integer and rational number

properties:- closure, commutative , associative, distributive and with one example

Dear Student,

Please find below the solution to the asked query:

Closure property of natural numbers :

We know natural numbers : 1 , 2 , 3 , 4 , 5 , . . .

And

If a set has the closure property under a particular operation, then we say that the set is " closed under the operation "   .

So,

For addition :  3 + 4 =  7  (  Here 3 , 4 and 7 all are natural numbers ) , So Natural numbers closed under the operation of addition .

For multiplication :  3 $\times$ 4 =  12  (  Here 3 , 4 and 12 all are natural numbers ) , So Natural numbers closed under the operation of multiplication .

For Subtraction :  3 - 2 = 1 ( Here 1 , 2  and 3 all are natural numbers )

And

3 - 4 =  - 1  (  Here - 1 is not a natural numbers ) , Since the subtraction of two natural numbers does not always result in a natural number, So natural number does not closed under the operation of Subtraction .

And

For division :  6 $÷$ 2 = 3 ( Here 2 , 3  and 6 all are natural numbers )

And

3 $÷$ 4 =  $\frac{3}{4}$  (  Here $\frac{3}{4}$ is not a natural numbers ) , Since the division of two natural numbers does not always result in a natural number, So natural number does not closed under the operation of division .

Such questions are made for enhancing the self creative skills and should be tried answering on your own. Try to find different properties for different type of numbers by yourself and if still have any doubt kindly get back to us so that we could help you precisely .

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