Question

give example of
closure
property of
division​

Answer 1

Answer:

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).

Answer 2

Answer:

The set of real numbers is closed under addition. If you add two real numbers, you will get another real number. There is no possibility of ever getting anything other than another real number.

 

5 + 12 = 17

2.5 + 3.4 = 5.9

 

3½ + 6 = 9½

closure add

   

expin2

The set of integers {... -3, -2, -1, 0, 1, 2, 3 ...} is NOT closed under division.

 

5 ÷ 2 = 2.5

Since 2.5 is not an integer, closure fails.

There are also other examples that fail.

   

one  

All that is needed is ONE counterexample

to prove closure fails.

expin3

The set of real numbers is closed under multiplication. If you multiply two real numbers, you will get another real number. There is no possibility of ever getting anything other than another real number.

 

4 x 5 = 20

1.5 x 2.1 = 3.15

 

3½ x 2½ = 8¾

example

The set of real numbers is NOT closed under division.

 

3 ÷ 0 = undefined

Since "undefined" is not a real number, closure fails.

 

Division by zero is the ONLY case where closure fails for real numbers.