Max and Emma are discussing their math homework and disagree on the answer for one question. Max says that integers are closed u
nder division because 8 divided by 2 is 4. Emma disagrees and says integers are not closed under division because 7 divided by 2 is 3.5, which is not an integer. Who is correct?
A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation.
A closure property is a certain rule that holds <u>if it is true for all elements of a set under the given operation</u> and a closure property does not hold <u>if there is at least one pair of elements that do not follow the closure property under the given operation.</u>
Therefore, Emma is correct, because you can find a counterexample (7:2=3.5) that gives you a non-integer answer.
