The following functional dependencies are given :
$$\eqalign{ & AB \to CD,\,AF \to D,\,\,DE \to F, \cr & C \to G.\,\,\,\,\,\,\,\,\,\,F \to E.\,\,\,\,\,\,\,\,\,G \to A. \cr} $$

Which one of the following options is false?

Consider the relation enrolled (student, course) in which (student, course ) is the primary key, and the relation Paid (student, amount) where student is the primary key. Assume no null values and no foreign keys or integrity constraints. Assume that amounts $$6000, 7000, 8000,9000$$ and $$10000$$ were each paid by $$20$$% of the students. Consider these query plans (Plan $$1$$ on left, Plan $$2$$ on right) to ''List all courses taken by students who have paid more than $$x''$$.

A disk seek takes $$4ms$$, disk data transfer bandwidth is $$300MB/s$$ and checking a tuple to see if amount is greater than $$x$$ takes $$10\mu s.$$ Which of the following statements is correct?

Consider a relation scheme $$R = \left( {A,\,B,\,C,\,D,\,E,\,H} \right)$$ on which the following functional dependencies hold: $$\left\{ {A \to B,\,\,BC \to D,\,\,E \to C,\,\,D \to A} \right\}.$$ What are the candidate keys of $$R?$$

In a schema with attributes $$A, B, C, D,$$ and $$E,$$ following set of functional dependencies are given
$$\eqalign{ & \,\,\,A \to B \cr & \,\,\,A \to C \cr & CD \to E \cr & \,\,\,B \to D \cr & \,\,\,E \to A \cr} $$

Which of the following functional dependencies is NOT implied by the above set?