Consider a database relation $R$ with attributes ABCDEFG , and having the following functional dependencies:

$$ \mathrm{A} \rightarrow \mathrm{BCEF} \quad \mathrm{E} \rightarrow \mathrm{DG} \quad \mathrm{BC} \rightarrow \mathrm{~A} $$

Which of the following statements is/are correct?

Consider the following tables, Loan and Borrower, of a bank.

Query: $\quad \pi_{\text {branch_name, customer_name }}$ (Loan $\triangleright \triangleleft$

Borrower) $\div \pi_{\text {branch_name }}$ (Loan)

where $\triangleright \triangleleft$ denotes natural join.

The number of tuples returned by the above relational algebra query is

__________

Suppose $X$ and $Y$ are random variables. The conditional expectation of $X$ given $Y$ is denoted by $E[X \mid Y]$. Then $E[E[X \mid Y]]$ equals

The sum of the elements in each row of $A \in \mathbb{R}^{n \times n}$ is 1 . If $B=A^3-2 A^2+A$, which one of the following statements is correct (for $x \in \mathbb{R}^n$ )?