Question

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

Explanation:

(a) Step1: Identify set hierarchy

Whole numbers ⊂ Integers ⊂ Rational numbers; Irrational numbers are disjoint from Rational numbers.

(a) Step2: Label Venn diagram

Innermost (smallest set): Whole numbers; Middle: Integers; Outermost: Rational numbers; Right region: Irrational numbers.

(b) Step1: Evaluate first statement

Irrational numbers ≠ fractions/integers → "No irrational numbers are integers" is True.

(b) Step2: Evaluate second statement

Whole numbers are rational → "All whole numbers are irrational" is False.

(b) Step3: Evaluate third statement

Whole numbers are rational → "Some whole numbers not rational" is False.

(b) Step4: Evaluate fourth statement

Rational numbers (e.g., 1/2) ≠ whole numbers → "Some rational not whole" is True.

Answer:

(a) Innermost circle: Whole numbers; Middle circle: Integers; Outermost circle: Rational numbers; Right rectangle: Irrational numbers
(b) 1. True; 2. False; 3. False; 4. True