Question

(a) use the names of the sets to label the regions of the venn - diagram. names of the sets whole numbers rational numbers integers (b) true or false? statement true false there are whole numbers that are not integers. there are rational numbers that are not whole numbers. all rational numbers are integers. all integers are whole numbers.

Explanation:

Step1: Recall set - relationships

Whole numbers are non - negative integers (0, 1, 2, 3, ...). Integers include positive and negative whole numbers and 0 (-3, - 2, -1, 0, 1, 2, 3, ...). Rational numbers are numbers that can be written as a fraction $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b
eq0$.

Step2: Label the Venn - diagram

The innermost circle is labeled "Whole numbers". The middle circle (which contains the whole - numbers circle) is labeled "Integers". The outermost circle (which contains the integers circle) is labeled "Rational numbers".

Step3: Evaluate the statements

1. All whole numbers are integers. So, the statement "There are whole numbers that are not integers." is False.
2. Rational numbers include fractions like $\frac{1}{2}$ which are not whole numbers. So, the statement "There are rational numbers that are not whole numbers." is True.
3. Rational numbers like $\frac{1}{2}$ are not integers. So, the statement "All rational numbers are integers." is False.
4. Integers include negative numbers, while whole numbers do not. So, the statement "All integers are whole numbers." is False.

Answer:

(a) Innermost circle: Whole numbers; Middle circle: Integers; Outermost circle: Rational numbers
(b)

1. False
2. True
3. False
4. False