Although SQL does not support functional dependency constraints, if thedatabase system supports constraints on materialized views, and materialized views are maintained immediately, it is possible to enforce functional dependency constraints in SQL. Given a relation r(A, B, C), explain how constraints on materialized views can be used to enforce the functional dependency B → C.

The division operator of relational algebra, “÷”, is defined as follows. Let r(R)and s(S) be relations, and let S ⊆ R; that is, every attribute of schema S isalso in schema R. Given a tuple t, let t[S] denote the projection of tuple t onthe attributes in S. Then r ÷ s is a relation on schema R − S (that is, on theschema containing all attributes of schema R that are not in schema S). A tuplet is in r ÷ s if and only if both of two conditions hold:• t is in ΠR−S(r)• For every tuple ts in s, there is a tuple tr in r satisfying both of the following:a. tr[S] = ts[S]b. tr[R − S] = tGiven the above definition:a. Write a relational algebra expression using the division operator to findthe IDs of all students who have taken all Comp. Sci. courses. (Hint:project takes to just ID and course id, and generate the set of all Comp.Sci. course ids using a select expression, before doing the division.)b. Show how to write the above query in relational algebra, without usingdivision. (By doing so, you…

Consider the relational schemas given below and the respective sets of functional dependencies valid in the schemas. R(A,B, C,D, E, H) Functional Dependency: A → B, BC → D,E → C,D → A (i) Find all the minimal super key of the relational table R. List the derivations of all minimal keys. Identify the highest normal form of the relational R. Remember that the identification of a normal form requires analysis of the valid functional dependencies. Decompose the relational table R into minimal number of normalized relational tables in BCNF. Remember to indicate the primary key and foreign keys (if any). (ii) (iii)

Give an SQL schema definition for the employee database of Figure 3.19.Choose an appropriate domain for each attribute and an appropriate primarykey for each relation schema. Include any foreign-key constraints that might beappropriate.