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Q: Are odd numbered sets closed under addition and multiplication?

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Yes

Yes they are closed under multiplication, addition, and subtraction.

The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.

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.

If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.

Yes. The empty set is closed under the two operations.

Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.

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

They form a closed set under addition, subtraction or multiplication.

The set of rational numbers is closed under all 4 basic operations.

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

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