Let's define the sets:
Integers: The set of all whole numbers.
Rational: Numbers that can be written as the quotient of two integer numbers.
Natural: The set of the positive integers.
Whole numbers: All the numbers that can be made by adding (or subtracting) 1 a given number of times.
Then:
2 is a:
Whole number because 1 + 1 = 2 (then it is also a integer)
We can write 2 = 4/2
Then 2 is the quotient of two integer numbers, then it is rational.
2 is positive and is an integer, then it is a natural number.
Then number 2 is an example of all four sets.
If we also want to include a negative number, we can use -3
-3 is an integer, is a whole number, and 9/-3 = -3, then it is also a rational number.
Now, answering the questions:
a) We can use only one example for all four sets, but in this case i gave 2.
b) in the same way that i prove that 2, a positive integer, belongs to the four sets, we can do the same for every positive integer, then:
Positive integers belong to:
The set of integers.
The set of natural numbers.
The set of rational numbers.
The set of whole numbers.
