Question

If there are two statements-
p: every fraction is a rational number.
q: every rational number is a fraction.
Then which of the following is correct?
(a) p is true and q is false
(b) p is false and q is true
(c) Both p and q are true
(d) Both p and q are false

Answer 1

Hint: To solve this problem, we should know the basics of fractions and a rational number. To select the correct option, we will try to understand the difference between fractions and a rational number. This will help in getting the required answer.

Complete step-by-step answer:
Before answering the question, we will try to understand about the terms fraction and rational numbers briefly (which will help us to solve the problem). Fractions represent equal parts of a whole or a collection. Thus, examples of fractions include $\dfrac{5}{4},\dfrac{2}{3},\dfrac{1}{1},\dfrac{4}{5},\dfrac{3}{8}$. Here, the number on the top is the numerator and the bottom number is the numerator. Both these numbers should be whole numbers (numbers like 0,1,2 and so on) and the denominator should not be 0.

A rational number is one which can be expressed in the form $\dfrac{a}{b}$, where a and b are any integers but b is not zero. For example, $\dfrac{-4}{5},\dfrac{5}{6},\dfrac{8}{5}$. Thus, the only difference is that numerator and denominator can be integers, thus they can also have negative values (this was not possible for fractions). Thus, fractions are basically a subset of rational numbers. Thus, all fractions are rational numbers but the inverse is not true.
Hence, the correct option is (a) p is true and q is false.

Note: In solving problems related to finding the difference between various types of numbers, it is extremely important to know the definition of each term accurately. Thus, it is important to distinguish between natural, whole, rational, fractions, irrational numbers, etc. and know the differences between each type.