Q1:Write the following queries in relational algebra, using the university schema (chapter6):
a) Find the titles of courses in the Comp. Sci. department that have 3 credits.
b) Find the highest salary of any instructor.
Q.2. Let the following relation schemas be given:
R = (A, B,C) and S = (D, E, F)
Let relations r(R) and s(S) be given. Give an expression in the tuple relational calculus that is equivalent to each of the following:
a) ∏ A(r )
b) σ B =17 (r )
Q3: Use Armstrong's axioms to prove the soundness of the pseudo transitivity rule.
If α → β and γ β → δ, then α γ → δ.
(1 Mark)
Q.4. Compute the closure of the following set F of functional dependencies for relation schema r (A, B, C, D, E).
A→BC
CD→E
B→D
E→A
(NOTE: list at least 6 members of F+)
Q5. Find candidate keys for the relation R(ABCD) having following FD's
AB→CD, C→A, D→A