Question

(a) use the names of the sets to label the regions of the venn
names of the sets
whole numbers
rational numbers
integers

(b) true or false?
statement\ttrue\tfalse
there are whole numbers that are not integers.\t\t
there are rational numbers that are not whole numbers.\t\t
all rational numbers are integers.\t\t
all integers are whole numbers.\t\t

Explanation:

Part (a)

Step1: Identify set hierarchy

Whole numbers are a subset of integers, which are a subset of rational numbers.

Step2: Label innermost circle

Innermost circle: Whole numbers

Step3: Label middle circle

Middle circle: Integers

Step4: Label outermost rectangle

Outermost rectangle: Rational numbers

1. Whole numbers are a subset of integers, so all whole numbers are integers.
2. Rational numbers include fractions (e.g., $\frac{1}{2}$) that are not whole numbers.
3. Rational numbers include non-integer values like $\frac{1}{3}$, so not all rationals are integers.
4. Integers include negative numbers (e.g., -1) which are not whole numbers.

Answer:

• Innermost circle: Whole numbers
• Middle circle: Integers
• Outermost rectangle: Rational numbers

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Part (b)