Question

(a) use the names of the sets to label the regions of the venn diagram.
names of the sets
whole numbers
rational numbers
irrational numbers
integers
(b) true or false?
statement\ttrue\tfalse
no whole numbers are irrational numbers.
all irrational numbers are integers.
some whole numbers are not integers.
some integers are not rational numbers.

Explanation:

Step1: Recall number - set relationships

Whole numbers are non - negative integers (0, 1, 2, ...). Integers are whole numbers and their negative counterparts (...,- 2,-1,0,1,2,...). Rational numbers are numbers that can be written as a fraction $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b
eq0$. Irrational numbers cannot be written as a fraction.

Step2: Label Venn - diagram regions

The innermost circle can be labeled "Whole numbers". The next - larger circle can be labeled "Integers" (since whole numbers are a subset of integers). The largest circle can be labeled "Rational numbers" (since integers are a subset of rational numbers). The region outside the largest circle is labeled "Irrational numbers".

Step3: Evaluate statements

1. Whole numbers are rational (can be written as a fraction with denominator 1), so no whole numbers are irrational. This statement is True.
2. Irrational numbers cannot be written as a fraction and integers can be written as a fraction with denominator 1. So, all irrational numbers are not integers. This statement is False.
3. Whole numbers are a subset of integers, so all whole numbers are integers. This statement is False.
4. All integers are rational (can be written as $\frac{n}{1}$ where $n$ is an integer). So, this statement is False.

Answer:

(a) Innermost circle: Whole numbers; Middle - sized circle: Integers; Largest circle: Rational numbers; Region outside largest circle: Irrational numbers
(b)

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