yes
It depends, many people do count 0 as a natural number, but MOST do not. So for most HS text book, the answer is NO, all whole numbers are not natural numbers and the reason is 0 is a whole number but not a natural number.
Yes all counting numbers are whole numbers, but the reverse is not true (zero!)
true
That's false.
That depends - unfortunately, "whole number" is ambiguous, and can mean different things to different people. If by "whole number" you mean "natural number", then both are of course the same. If you choose to include negative numbers in your definition of "whole number", i.e., whole numbers = integers, then the two sets are not the same, and the proposed statement is false.
yes
true
Yes, no irrational numbers are whole numbers.
Yes, it is true.
It depends, many people do count 0 as a natural number, but MOST do not. So for most HS text book, the answer is NO, all whole numbers are not natural numbers and the reason is 0 is a whole number but not a natural number.
No, integers are positive and negative whole numbers
If the two numbers are both whole numbers then yes
true
Yes all counting numbers are whole numbers, but the reverse is not true (zero!)
The density property does not hold for odd numbers in the same way it does for the set of all integers or real numbers. While there are infinitely many odd numbers, they are not densely packed within the integers; there are gaps between them (specifically, every even integer separates two odd integers). Thus, between any two odd numbers, there are even integers, indicating that odd numbers do not form a dense subset of the integers.
True.
True.