Question

If 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

The correct option is A p is true and q is false.

Fraction is defined as a part of a whole thing. Every fraction is of the form $\frac{m}{n}$ where $m$ is a whole number and $n$ is a natural number.

Rational number is defined as the number of the form $\frac{a}{b}$ where $a$ and $b$ are integers and $b\ne 0$.

Since all whole numbers and natural numbers are present in set of integers every fraction is a rational number. Examples : $\frac{4}{5},\frac{4}{7}$

So, the statement $p$ is true.
But every rational number is not a fraction. Examples : $\frac{3}{-4},\frac{17}{-16}$. Here the denominators are not natural numbers and hence they are not fractions.
So, the statement $q$ is false.