Answer:
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.
1) The fewest number of points that must be plotted to have examples of all four sets of numbers is; 2 points
2) The sets among the options that positive integers belong are;
Options A, B, C & D
1) Numbers are generally classified into 2 main groups namely;
- Rational numbers
- Irrational numbers
All the four examples listed are types of rational numbers.
Now, by definition, positive integers are also referred to as whole numbers and natural numbers. Thus, one plot can show, whole numbers and natural numbers.
Meanwhile another plot will be required to show integers because integers can either be positive and negative and could include fractions.
Thus, fewest number of points you must plot to have examples of all four sets of numbers is 2 points.
2) From above we saw that positive integers are types of rational numbers. We also saw that positive integers are also natural numbers and whole numbers. Thus, all the options apply to positive integers.
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