Consider the following relational schema along with all the functional dependencies that hold on them.

$$\begin{aligned} & R 1(A, B, C, D, E):\{D \rightarrow E, E A \rightarrow B, E B \rightarrow C\} \\ & R 2(A, B, C, D):\{A \rightarrow D, A \rightarrow B, C \rightarrow A\} \end{aligned}$$

Which of the following statement(s) is/are TRUE?

Consider a relational schema team(name, city, owner), with functional dependencies \{name $\rightarrow$ city, name $\rightarrow$ owner}.

The relation team is decomposed into two relations, $t 1$ (name, city) and $t 2$ (name, owner). Which of the following statement(s) is/are TRUE?

A functional dependency $F: X \to Y$ is termed as a useful functional dependency if and only if it satisfies all the following three conditions:

• $X$ is not the empty set.
• $Y$ is not the empty set.
• Intersection of $X$ and $Y$ is the empty set.

The symbol → indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?