Question

Use the Venn diagram to determine which statements are true. (Choose 3)
Responses

A Some irrational numbers are integers.Some irrational numbers are integers.

B All rational numbers are integers.All rational numbers are integers.

C Some rational numbers are whole numbers.Some rational numbers are whole numbers.

D Some, but not all, natural numbers are rational numbers.Some, but not all, natural numbers are rational numbers.

E All rational and irrational numbers are real numbers.All rational and irrational numbers are real numbers.

F Rational numbers and irrational numbers have no numbers in common.

Answer 1

Correct choices: C, E, F.

- C true: some rational numbers are whole numbers (examples: 0, 1, 2 are whole numbers and rational).
- E true: every rational and every irrational number is a real number (rationals ∪ irrationals = ℝ).
- F true: rational and irrational numbers are disjoint — no number is both rational and irrational.

(The other statements are false: integers are rational, not irrational; not all rationals are integers; and all natural numbers are rational, not "some but not all".)