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# 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.

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

(c) I is false, II is true