Question

take a least five pairs of integers and check whether they are closed under division​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

The set of integers is not closed under the operation division.

Step-by-step explanation:

Given : select 5 pairs of integers.

To find :the pairs of integers are closed under division.

Solution:

Closure property under division: In we consider integers and  we divide any two integers the answer should also and always be an integer. It is said to be closed under division. If the answer is not an integer it is not closed under division.

Answer determines whether it is closed or not.

(1) Let 8,4  be a pair of integers.

when we divide  8÷4 =2, 2 is an integer.

(2) 2,5 be a pair of integers.

   2÷5 = 0.4 .

0.4 is not an integer.

(3) 4,-2

 4÷(-2) = -2, which is an integer.

(4) -5, 10

 (-5)÷(10) = 1÷(-2) =  -0.5, which is not an integer.

(5) -16,-4

(-16)÷(-4) = 4, which is an integer.

So the set of integers is not closed under the operation division because the division of integers is not always integer.

Thus closure property does not hold under division of integers.

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