It depends on your definition of whole numbers. The classic definition of whole numbers is the set of counting numbers and zero. In this case, the set of whole numbers is not closed under subtraction, because 3-6 = -3, and -3 is not a member of this set. However, if you use whole numbers as the set of all integers, then whole numbers would be closed under subtraction.
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.
Integer
Integers.
That is called the set of "integers".
The set of whole numbers is represented by Z.
The set of integers (ℤ) is the set of the positive whole numbers and their additive opposites (the negative whole numbers).
The set of integers includes the set of whole numbers. The set of rational numbers includes the sets of whole numbers and integers.
Actually the set of integers is the same as the set of whole numbers since the whole numbers include negative whole numbers and zero.
The set of integers is the same as the set of whole numbers.
The set of natural numbers is a subset of the set of whole numbers. The set of whole numbers is a subset of the set of integers. So the set of integers is the largest of these three sets.
Zero (0) is in the set of whole number. The only difference between the set of whole numbers and counting numbers is that the whole numbers contain zero. {0,1,2,3...}
Apart from zero (which is its own opposite), the opposites of whole numbers are also whole numbers. You have the set of whole numbers which is also known as the set of integers.
If you mean larger by "the set of whole numbers strictly contains the set of natural numbers", then yes, but if you mean "the set of whole numbers has a larger cardinality (size) than the set of natural numbers", then no, they have the same size.
Whole numbers and natural numbers are the exact same, except that whole numbers include zero
Whole numbers are the set of natural or counting numbers inclding zero
No, it is not.