Question

Determine whether the set is closed for the given operation.

explain your reasoning. -- -the set of integers for division
-the set of positive integers for subtraction.

Answer 1

Closure Property for the set of integers for Subtraction

Take two integers,

A=6

B=9

A-B

=6-9

= -3

Which is also an Integer.Hence Closure Property is satisfied by Integers with respect to Subtraction.

⇒Closure Property for the set of integers for Division

Take two integers,

A=6

B=9

`\rightarrow (A)/(B)\\\\=(6)/(9)\\\\=(2)/(3)-----\text{Not an Integer}`

Which is not an Integer.Hence Closure Property is not satisfied by Integers with respect to Division.