Let the set of functional dependencies

F = {QR → S, R → P, S → Q}

hold on a relation schema X = (PQRS). X is not in BCNF. Suppose X is decomposed into two schemas Y and Z, where Y = (PR) and Z = (QRS).

Consider the two statements given below.

I. Both Y and Z are in BCNF
II. Decomposition of X into Y and Z is dependency preserving and lossless

Which of the above statements is/are correct?

Consider an Entity-Relationship (ER) model in which entity sets E₁ and E₂ are connected by an m : n relationship R₁₂. E₁ and E₃ are connected by a 1 : n (1 on the side of E₁ and n on the side of E₃) relationship R₁₃.

E₁ has two single-valued attributes a₁₁ and a₁₂ of which a₁₁ is the key attribute. E₂ has two single-valued attributes a₂₁ and a₂₂ of which a₂₁ is the key attribute. E₃ has two single-valued attributes a₃₁ and a₃₂ of which a₃₁ is the key attribute. The relationships do not have any attributes.

If a relational model is derived from the above ER model, then the minimum number of relations that would be generated if all the relations are in 3NF is _______.

Given the following two statements:
$$S1:$$ Every table with two single-valued attributes is in $$1NF, 2NF, 3NF$$ and $$BCNF.$$
$$S2:$$ $$AB \to C,\,\,D \to E,\,\,E \to C$$ is a minimal cover for the set of functional dependencies $$AB \to C,$$ $$D \to E,\,\,AB \to E,\,\,E \to C.$$

Which one of the following is CORRECT?

Relation $$R$$ has eight attribution $$ABCDEFGH.$$ Fields of $$R$$ contain only atomic values.
$$F = \left\{ {CH \to G,\,\,A \to BC,\,B \to CFH,\,\,E \to A,\,\,F \to EG} \right\}$$ set of functional dependencies $$(FDs)$$ so that $${F^ + }$$ is exactly the set of $$FDs$$ that hold for $$R.$$

How many candidate keys does the relation $$R$$ have?