If Q denotes the set of all rational numbers and $f\bigg(\large\frac{p}{q}\bigg)$$=\sqrt {p^2-q^2}$ for any $\large\frac{P}{q}$$\in Q$ , then observe the following statements.

Question

I. $f \bigg(\large\frac{p}{q}\bigg)$ is real for each $\large\frac{p}{q}$$\in Q$

II. $f \bigg(\large\frac{p}{q}\bigg)$ is complex number for each $\large\frac{p}{q}$$\in Q$

Which of the following is correct?

(a) Both I and II are true

(b) I is true, II is false

(c) I is false, II is true

(d) Both I and II are false