If you can never, by multiplying two whole numbers, get anything but another whole number back as your answer, then, YES, the set of whole numbers must be closed under multiplication.
l think multiplication
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. That means that the product of two whole numbers is defined, and that it is again a whole number.
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
They form a closed set under addition, subtraction or multiplication.
Yes, it is closed. This means that if you multiply two even number, you again get a number within the set of even numbers.
Because if X and Y are any two whole number, then X*Y is also a whole number. Always.