Question

P: Every fraction is a rational number
Q: Every rational number is a fraction.

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

Consider a fraction $\frac{3}{8}$ and rational number $-\frac{2}{7}$.
We know by definition of a rational number, that $\frac{3}{8}$ is also a rational number. This implies the statement P is true.
But by definition of a fraction, $-\frac{2}{7}$ is not a rational number since the value $-2$ is not a natural number. This means that the statement Q is false.