Which of the following represents a function?

The number of relations $R$ from an $m$-element set $A$ to an $n$-element set $B$ satisfying the condition $(a, b_1) \in R, (a, b_2) \in R \Rightarrow b_1 = b_2$ for $a \in A, b_1, b_2 \in B$ is

If $Q$ denotes the set of all rational numbers and $f\left(\frac{p}{q}\right)=\sqrt{p^2-q^2}$ for any $\frac{p}{q} \in Q$, then observe the following statements.
$I$. $f\left(\frac{p}{q}\right)$ is real for each $\frac{p}{q} \in Q$.
$II$. $f\left(\frac{p}{q}\right)$ is a complex number for each $\frac{p}{q} \in Q$.
Which of the following is correct?

Let $A = \{a, b, c, d\}$ and $B = \{1, 2, 3\}$. The relations $R_1, R_2, R_3, R_4$ are defined as follows:
$R_1 = \{(a, 1), (b, 2), (c, 1), (d, 2)\}$
$R_2 = \{(a, 1), (b, 1), (c, 1), (d, 1)\}$
$R_3 = \{(a, 2), (b, 3), (c, 2), (d, 2)\}$
$R_4 = \{(a, 1), (b, 2), (a, 2), (d, 3)\}$
Which of the following is true?

The function $t$,which maps temperature in degree Celsius into temperature in degree Fahrenheit,is defined by $t(C) = \frac{9C}{5} + 32$. Find the value of $C$ when $t(C) = 212$.

Let $f$ be the subset of $Z \times Z$ defined by $f = \{(ab, a+b) : a, b \in Z\}$. Is $f$ a function from $Z$ to $Z$? Justify your answer.