Which one of the following statements is/are false?
A. Every whole number is a natural number.
B. Every integer is a rational number.
C. Every rational number is an integer
D. Every integer is a whole number.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A, C and D only
The number sets fit inside one another: natural numbers (1, 2, 3, ...) ⊂ whole numbers (0, 1, 2, ...) ⊂ integers (..., −2, −1, 0, 1, 2, ...) ⊂ rational numbers (numbers of the form \(\frac{p}{q}\), \(q\ne0\)). A larger set is not always inside a smaller one, and one counter-example makes such a statement false.
A. Every whole number is a natural number. Incorrect. 0 is a whole number but not a natural number, so the statement is false.
B. Every integer is a rational number. Correct. Any integer \(n\) can be written as \(\frac{n}{1}\), so it is rational; the statement is true.
C. Every rational number is an integer Incorrect. \(\frac{1}{2}\) is rational but not an integer, so the statement is false.
D. Every integer is a whole number. Incorrect. Negative integers such as −3 are not whole numbers, so the statement is false.