Question

THINKABOUT ITDetermine Closure of the IntegersOfUnder what operations are the set of integersclosed? Explain your answer.DONE

Answer 1

We say that a set A is closed under an operation * if for a and b in the set

`a\ast b\to\text{ in the set A}`

The set of integers consists of

`\ldots,-3,-2,-1,0,1,2,3,\ldots`

Notice that they are closed under addition, subtraction, and multiplication (the addition, subtraction, or multiplication of two integers is itself an integer).

However, as for the division,

`\begin{gathered} (4)/(2)=2\to\text{ integer} \\ (2)/(3)=0.6666\ldots\to\text{ not integer} \end{gathered}`

Therefore, the set is not closed under division because the division of two integers could or could not be an integer.