Consider a rooted n node binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having exactly 4 nodes O(n^a Log^bn ). Then the value of a + 10b is _________

Consider the relation schema $$R = \left( {E,\,F,\,G,\,H,\,I,\,J,\,K,L,\,M,\,N} \right)$$ and the set of functional dependencies $$\left\{ {\left\{ {E,F} \right\} \to \left\{ G \right\},\left\{ F \right\}} \right.$$
$$ \to \left\{ {I,J} \right\},\left\{ {E,H} \right\} \to \left\{ {K,L} \right\},\left\{ K \right\}$$
$$ \to \left\{ M \right\},\left\{ L \right\}$$
$$ \to \left. {\left\{ N \right\}} \right\}$$ on $$R.$$ What is the key for $$R?$$

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?

Given the following statements:

S1: A foreign key declaration can always be replaced by an equivalent check assertion in SQL.

S2: Given the table R(a,b,c) where a and b together form the primary key, the following is a valid table definition.

CREATE TABLE S (
 a INTEGER,
 d INTEGER,
 e INTEGER,
 PRIMARY KEY (d),
 FOREIGN KEY (a) references R)

Which one of the following statements is CORRECT?