An example would be 2 ÷ 4 = 0.5
A counter example would be 4 ÷ 2 = 2
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Add two positive integers and you ALWAYS have a positive integers. The positive integers are closed under addition.
You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
division
yes, because an integer is a positive or negative, rational, whole number. when you subject integers, you still get a positive or negative, rational, whole number, which means that under the closure property of real numbers, the set of integers is closed under subtraction.