Question

Which of the following statements is a tautology and why is it that right answer

A. Integers are rational numbers.
B. Whole numbers are natural numbers.
C. Rational numbers are irrational.
D. Irrational numbers are integers.

Answer 1

I think the answer is A

Answer 2

Answer: Well, we know that N ⊂ Z ⊂ Q ⊂ R

This means that the naturals are included in the integers, the integers (and the naturals) are included in the rationals, and the rationals are included in the reals.

Then, A is a tautology.

B is false, because the 0 is not a natural number,

C is false, because the irrational numbers are the complement of the rational numbers.

D you can see that the integers are irrationals, but not all irrationals are integers, so this also is false.