Let T be a depth-first search tree in an undirected graph G. Vertices u and v are leaves of this tree T. The degrees of both u and v in G are at least 2. Which one of the following statements is true?

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?

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 account (customer, balance) where customer is a primary key and there are no null values. We would like to rank customers according to decreasing balance. The customer with the largest balance gets rank 1. Ties are not broke but ranks are skipped: if exactly two customers have the largest balance they each get rank 1 and rank 2 is not assigned.

Query1:
  Select A.customer, count(B.customer)
  From account A, account B
  Where A.balance <=B.balance
  Group by A.customer

Query2:
  Select A.customer, 1+count(B.customer)
  From account A, account B
  Where A.balance < B.balance
  Group by A.customer

Consider these statements about Query1 and Query2.

1. Query1 will produce the same row set as Query2 for some but not all databases.

2. Both Query1 and Query2 are correct implementation of the specification

3. Query1 is a correct implementation of the specification but Query2 is not

4. Neither Query1 nor Query2 is a correct implementation of the specification

5. Assigning rank with a pure relational query takes less time than scanning in decreasing balance order assigning ranks using ODBC.

Which two of the above statements are correct?