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Q: Why are odd integers closed under multiplication but not under addition?

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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.

No.

Yes!

negetive integers are not closed under addition but positive integers are.

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).

Yes

yes

The set of integers is not closed under multiplication and so is not a field.

Yes.

No, it is not.

That is correct, the set is not closed.

Yes it is.

They are not the same!The set of integers is closed under multiplication but not under division.Multiplication is commutative, division is not.Multiplication is associative, division is not.

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

addition

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. The empty set is closed under the two operations.

1 No. 2 No. 3 Yes.

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

Any time you add integers, the sum will be another integer.

Add two positive integers and you ALWAYS have a positive integers. The positive integers are closed under addition.

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.

No. 1 + 3 = 4, which is not odd. In fact, no pair of odds sums to an odd. So the set is not closed under addition.