Question

The set of fractions between the natural numbers 3 and 1 is a:
A. Finite Set
B. Null Set
C. Infinite Set
D. Singleton Set

Answer 1

Hint: Fractions can be formed by expressing two numbers as a ratio. Natural numbers are the set of numbers starting from 1 and continuing till infinity. Between 3 and 1, 2 is the natural number. Also, remember the fact that there are infinite fractions contained between 3 and 4. Now, using this data, we can choose the right option.

Complete step-by-step answer:
In the question, we are given two consecutive natural numbers 3 and 4 and we have to say that what is the set of fractions between 3 and 4 as a finite set, null set, infinite set or singleton set.
Before proceeding, we will first learn briefly about fractions.
A fraction represents a part of a whole or more, generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one half, eight fifth, three quarters. A common, vulgar or simple fraction, for example: \[\dfrac{1}{2},\dfrac{{17}}{2}\] consists of a numerator displayed above a line (or before a slash) and a non-zero denominator, displayed below or after the line. Numerator and denominator are also used in fractions that are not in common, including compound fraction and mixed numerals.
It's a fact that between two consecutive natural numbers there are an infinite number of fractions which exists. Hence, the set is an infinite set.
Thus, the correct option is ‘C’.

Note: Between any two consecutive natural numbers, the distance can be divided into infinite parts, also after selecting some parts one can form a fraction too which can be done in infinite ways. Considering options, a finite set is not possible as we know that there are infinite possibilities. Null set is also not possible, because we definitely have fractions between 3 and 1. A Singleton set is a set containing only 1 element, which is also not possible here.