What expression is a counterexample to the statement The whole numbers are closed under division

2 divided by 10th
10 divided by 2
Please explain to me which one is the correct

Your statement of

"The whole numbers are closed under division" is contradicted by 2 ÷ 10 .

btw , you probably did not mean 10th
since 2 ÷ a 10th
= 2 ÷ 1/10)
= 2 (10/1) = 20 , which would NOT be a counterexample.

In fact, it's an incorrect attempt, since you are supposed to be dealing with integers. 1/10 is not an integer, so you can't use it as a divisor.

To determine if the whole numbers are closed under division, we need to check if dividing any two whole numbers always results in another whole number. A counterexample would be an example that disproves the statement by providing a specific instance where the statement does not hold true.

Let's consider the given expressions:
1. 2 divided by 10th: This expression is equivalent to dividing 2 by 1/10 or 0.1. The result of this division is 20, which is not a whole number. Therefore, this expression serves as a counterexample to the statement.

2. 10 divided by 2: This expression is equivalent to dividing 10 by 2, resulting in 5. This is indeed a whole number. Therefore, this expression does not serve as a counterexample to the statement.

In conclusion, the first expression "2 divided by 10th" is a counterexample to the statement "The whole numbers are closed under division."