Yes. That means that the product of two whole numbers is defined, and that it is again a whole number.
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Yes.
whole numbers
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.
They form a closed set under addition, subtraction or multiplication.
Because if X and Y are any two whole number, then X*Y is also a whole number. Always.