True.
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False. The set of whole numbers is not closed under subtraction. Closure under subtraction means that when you subtract two whole numbers, the result is also a whole number. However, this is not always the case with whole numbers. For example, subtracting 5 from 3 results in -2, which is not a whole number.
False. Irrational numbers are real numbers.
There is some disagreement. Some people include zero in the set of natural numbers (like whole numbers), some people don't (like counting numbers).
Yes, no irrational numbers are whole numbers.
It is true and false. It cannot be proved.