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 E_{1} and E_{2} are connected by an m : n relationship R_{12}. E_{1} and E_{3} are connected by a 1 : n (1 on the side of E_{1} and n on the side of E_{3}) relationship R_{13}.

E_{1} has two single-valued attributes a_{11} and a_{12} of which a_{11} is the key attribute. E_{2} has two single-valued attributes a_{21} and a_{22} of which a_{21} is the key attribute. E_{3} has two single-valued attributes a_{31} and a_{32} of which a_{31} 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 _______.

$$S1:$$ 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?

$$F = \left\{ {CH \to G,\,\,A \to BC,\,B \to CFH,\,\,E \to A,\,\,F \to EG} \right\}$$ 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?