The correct answer is Option (2) → (B) only
To determine the correct statement, we need to understand the definitions and relationships between these sets of numbers.
Definitions of Number Sets:
- Natural Numbers ($N$): $\{1, 2, 3, 4, ...\}$ (Counting numbers starting from 1).
- Whole Numbers ($W$): $\{0, 1, 2, 3, 4, ...\}$ (Natural numbers plus zero).
- Integers ($Z$): $\{..., -2, -1, 0, 1, 2, ...\}$ (Whole numbers plus negative natural numbers).
- Rational Numbers ($Q$): Any number that can be expressed as a fraction $\frac{p}{q}$ (like $\frac{1}{2}, -5, 0.75$).
Analysis of Statements:
- (A) Every whole number is a natural number: Incorrect. The number 0 is a whole number, but it is not a natural number.
- (B) Every natural number is a whole number: Correct. All natural numbers ($1, 2, 3...$) are included in the set of whole numbers.
- (C) Every integer is a whole number: Incorrect. Negative integers (like $-1, -2, -3$) are not whole numbers.
- (D) Every rational number is a whole number: Incorrect. Numbers like $\frac{1}{2}$ or $0.5$ are rational, but they are not whole numbers.
Conclusion: Only statement (B) is true. |
