Q. 1055.0( 1 Vote )

State whether the statements are True or False.

Integers are closed under division.

Answer :

We have been given that, integers are closed under division.

Let it be a true statement.

Then, assume two integers, say 5 and 9.

Now, divide the integers.

According to our assumption, 5/9 is an integer.

But according to the definition of integers, integers are whole numbers that can be positive, negative or zero.

While, 5/9 is a positive but not whole number.

5/9 is not integer.

So, our assumption is wrong.

And we can say that integers are not closed under division as integer divided integer does not always give an integer.

Thus, this is a false statement.

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