Write the following queries in relational algebra, using the university schema

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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

Resources:

Silberschatz, A., Korth, F., & Sudarshan, S. Database system concepts (6th Ed.).New York: McGraw Hill, 2010. ISBN # ISBN 0-07-352332-1

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