Question

Consider the following statements:
A) There exists a smallest natural number.
B) There exists a largest natural number.
C) Every rational number is also a real number.
D) Between two consecutive natural numbers, there is always a natural number.

• A. A only
• B. C only
• C. B and D only
• D. A and C only

Hint:

Remember: Natural numbers have a smallest element but no largest element, and there is no natural number between two consecutive natural numbers.

Answer 1

The Correct Option is D

Step 1: Analyze Statement A.
Natural numbers are defined as \( 1, 2, 3, 4, \dots \).
Clearly, the smallest natural number is \(1\).
Hence, Statement A is true.
Step 2: Analyze Statement B.
Natural numbers continue endlessly and do not terminate.
For any natural number \(n\), there always exists a natural number \(n+1\).
Therefore, there is no largest natural number.
Hence, Statement B is false.
Step 3: Analyze Statement C.
Rational numbers are numbers that can be written in the form \( \frac{p}{q} \), where \(p, q\) are integers and \(q \neq 0\).
All rational numbers lie on the real number line.
Thus, every rational number is a real number.
Hence, Statement C is true.
Step 4: Analyze Statement D.
Consecutive natural numbers differ by exactly 1.
For example, between 3 and 4, there is no natural number.
Therefore, it is not possible to find a natural number between two consecutive natural numbers.
Hence, Statement D is false.
Step 5: Final evaluation.
Statement A is true.
Statement B is false.
Statement C is true.
Statement D is false.
Therefore, the correct combination of true statements is A and C only.