No. Integers are not closed under division because they consist of negative and positive whole numbers. NO FRACTIONS!
No.
For a set to be closed under an operation, the result of the operation on any members of the set must be a member of the set.
When the integer one (1) is divided by the integer four (4) the result is not an integer (1/4 = 0.25) and so not member of the set; thus integers are not closed under division.
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Subtraction: Yes. Division: No. 2/4 = is not an integer, let alone an even integer.
addition
No.
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
No. For example: 2 and 6 are both members, but 6/2 = 3 is not; similarly 2 and 4 are both members but 2/4 = 0.5 is not (it is not an integer for starters).