Consider a relational database schema with two relations $R(P, Q)$ and $S(X, Y)$.

Let $E=\{\langle u\rangle \mid \exists v \exists w\langle u, v\rangle \in R \wedge\langle v, w\rangle \in S\}$ be a tuple relational calculus expression. Which one of the following relational algebraic expressions is equivalent to $E$ ?

Consider a relational database schema with a relation $R(A, B, C, D)$. If $\{A, B\}$ and $\{A, C\}$ are the only two candidate keys of the relation $R$, then the number of superkeys of relation $R$ is $\_\_\_\_$ . (answer in integer)

Consider the following Boolean expression of a function $F$ :

$$ F(P, Q)=(\bar{P}+Q) \oplus(\bar{P} Q) $$

Which of the following expressions is/are equivalent to $F$ ?

Consider the 8-bit signed integers $X, Y$ and $Z$ represented using the sign-magnitude form. The binary representations of $X$ and $Y$ are as follows:

$$ X: 10110100 \quad Y: 01001100 $$

Which of the following operations to compute $Z$ result(s) in an arithmetic overflow?