Question

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

Explanation:

Step1: Label Venn - diagram regions

The outermost region (outside all circles) represents non - rational numbers. The largest circle represents rational numbers. The middle - sized circle represents integers. The smallest circle represents whole numbers.

Step2: Analyze statements

1. Whole numbers are a subset of integers. So, the statement "There are whole numbers that are not integers" is False.
2. Rational numbers include fractions and decimals which are not whole numbers. So, the statement "All rational numbers are whole numbers" is False.
3. Integers include negative numbers which are not whole numbers. So, the statement "All integers are whole numbers" is False.
4. An integer \(n\) can be written as \(\frac{n}{1}\), so all integers are rational numbers. The statement "All integers are rational numbers" is True.

Answer:

(a) Outermost region: Non - rational numbers; Largest circle: Rational numbers; Middle - sized circle: Integers; Smallest circle: Whole numbers
(b)
There are whole numbers that are not integers: False
All rational numbers are whole numbers: False
All integers are whole numbers: False
All integers are rational numbers: True