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Assignment 2: 1. Consider the relation R (ABCDE) with following functional dependencies (FDs): (25 points) J = {A B, BC D, D BC, C A} A) Identify the...
- Assignment 2:
1. Consider the relation R (ABCDE) with following functional dependencies (FDs): (25 points)
J = {A →B, BC → D, D → BC, C → A}
A) Identify the candidate key of this relation.
B) Suppose the relation is decomposed into, R1 (AB) R2 (BCD) Does this decomposition have a lossless join? Justify your answer.
2. Given the following set of functional dependencies, determine the specified X-closure by applying Armstrong’s axioms. Show all work. (25 points)
A) F = {X → W, Y → Z, WZ → P}. Find XZ closure.
B) F= {ABC → D, A → C, EJ → GH, CJ → K}. Find AB closure.
C) F= {A → D, A→E, B → C, CD → F}. Find AB closure.
D) F= {ABC → DE, G → D, E → F, F → A}. Find E closure.
3. Let R be a relation schema defined as R (ABCDEFGH) with the following functional dependencies:
J = {ABC → EF, A→ D, D → BG, D → B, DG → EH}
Find the minimal cover for J. Show all work. (25 points)
4. Consider the relational schema R(ABCDEFGH) with FDs
J = {CD → F, EG → B, EG→A, EH → G, F → C}
Assume that J is already a minimum cover. Find a decomposition of R which preserves dependencies and is in third normal form. Show all work. (25 points)
