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Subtraction: Yes.

Division: No. 2/4 = is not an integer, let alone an even integer.

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Q: Is the set of even integers closed under subtraction and division?

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Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.

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.

Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.

addition

No; here's a counterexample to show that the set of irrational numbers is NOT closed under subtraction: pi - pi = 0. pi is an irrational number. If you subtract it from itself, you get zero, which is a rational number. Closure would require that the difference(answer) be an irrational number as well, which it isn't. Therefore the set of irrational numbers is NOT closed under subtraction.

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Yes.

1 No. 2 No. 3 Yes.

Yes, the set of integers is closed under subtraction.

Whole numbers subtraction: YesDivision integers: No.

Integers are closed under subtraction, meaning that any subtraction problem with integers has a solution in the set of integers.

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.

Yes.

No, they are not.

To be closed under an operation, when that operation is applied to two member of a set then the result must also be a member of the set. Thus the sets ℂ (Complex numbers), ℝ (Real Numbers), ℚ (Rational Numbers) and ℤ (integers) are closed under subtraction. ℤ+ (the positive integers), ℤ- (the negative integers) and ℕ (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.

Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.

They are closed under all except that division by zero is not defined.

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.