A-1 Armstrong Axioms a. Consider the relation R(L,M,N,O,P,Q) and a set of functional dependencies F =...

 

Transcribed Image Text:

A-1 Armstrong Axioms a. Consider the relation R(L,M,N,O,P,Q) and a set of functional dependencies F = {LNOM, MNLOP, NO, OPLN}. [2pt] Can we infer NP LM from F? Show your work [3pt] Can we infer NQ LO from F? Show your work b. [10pt] Consider R (O,P,Q,R,S,T) to be a relation schema, and let F = {O P, QO, PR Q, RS T} be a set of functional dependencies (FDs). Infer at least five new FDs by using Armstrong's axioms and their derived inference rules. You must use a different rule per answer A-2 Keys a. [5pt] Find all the candidate keys of the Relation R(ABCDE) with FD's: D C, CE A, D A, and AE D b. [5pt] Determine all the candidate and super keys of the relation R(ABCDEF) with FD's: {AEF C, BF C, EF D, ACDE F} c. [5pt] Consider the relation EMPLOYEE(ID, First, Last, Team, Dept, Salary) with the following set F of functional dependencies, Identify all the candidate keys of EMPLOYEE: ID First ID Last First, Last ID Last Team ID Dept ID Salary Salary Dept d. Given R(I, N, C, S) and F {IN, IC, IS, CS} [5pts] Calculate the closure of all possible subsets of attributes Hint: how many subsets a set has? Ignore the empty set. [2pts] Identify all super keys [3pts] Identify all candidate keys A-1 Armstrong Axioms a. Consider the relation R(L,M,N,O,P,Q) and a set of functional dependencies F = {LNOM, MNLOP, NO, OPLN}. [2pt] Can we infer NP LM from F? Show your work [3pt] Can we infer NQ LO from F? Show your work b. [10pt] Consider R (O,P,Q,R,S,T) to be a relation schema, and let F = {O P, QO, PR Q, RS T} be a set of functional dependencies (FDs). Infer at least five new FDs by using Armstrong's axioms and their derived inference rules. You must use a different rule per answer A-2 Keys a. [5pt] Find all the candidate keys of the Relation R(ABCDE) with FD's: D C, CE A, D A, and AE D b. [5pt] Determine all the candidate and super keys of the relation R(ABCDEF) with FD's: {AEF C, BF C, EF D, ACDE F} c. [5pt] Consider the relation EMPLOYEE(ID, First, Last, Team, Dept, Salary) with the following set F of functional dependencies, Identify all the candidate keys of EMPLOYEE: ID First ID Last First, Last ID Last Team ID Dept ID Salary Salary Dept d. Given R(I, N, C, S) and F {IN, IC, IS, CS} [5pts] Calculate the closure of all possible subsets of attributes Hint: how many subsets a set has? Ignore the empty set. [2pts] Identify all super keys [3pts] Identify all candidate keys