Question

If p:every fraction is a rational number and q:every rational number is a fraction,then which if the following options hold-
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-The rational number is expressed in the $\dfrac{p}{q}$ form where p and q are integers and where q≠0.Every fraction may not have integers in denominator and numerator.

Complete step-by-step answer:
We know that the rational number is defined as the expression written in the form of$\dfrac{p}{q}$ where p and q are integers and q≠0. Thus all rational numbers can be written in the form of fraction like $\dfrac{1}{2},\dfrac{{13}}{{15}},\dfrac{{58}}{{65}}$.But all the fractions are not rational number if the numerator or denominator is not an integer like in$\dfrac{\pi }{2},\dfrac{\pi }{4},\dfrac{{\sqrt 3 }}{4}$.These are all irrational numbers.
Hence,the correct answer is B.

Note: You can also prove this by considering a rational number and then explaining why it is a fraction and then considering a fraction which does not have integers as numerator or denominator and explaining why it is not a rational number.