Consider the following relations: n-nd# 10 b1 10 b2 11 b4 12 b3 13 b1 14 b3 c1 c

Question

Consider the following relations: n-nd# 10 b1 10 b2 11 b4 12 b3 13 b1 14 b3 c1 c2 c1 3 c1 C4 a). For this given situation, which of the following functions determine potentially be present in the relation? If not explain why by using two n-nd that break the function i. A B iv. B-A Can these reactions have candidate key? If yes find the keys, if not explain why not. 2) a) R(A, B, C, D) and S = {AB C, C D, D A} b) R(A, B, C, D) and S = {A B, B C, BD) i. Find the functional dependencys resulting from S ii. Find all keys in R. ii. Find all superkeys that are not keys in R

Explanation / Answer

first we see the what is candidate key:

the relation does not have two distinct tuples here tuples means rows or record with the same values.

question contains

A->B

B->C

C->B

B->A

C->A

all contains unique values consider it in pairs

like (A,B): (10,b1)(10,b2)(11,b4)(12,b3)(13,b1)(14,b3) all are different so here all are candidate keys.

2.functional dependency:

suppose if X in R said to be functionally determine another set of attributes Y also in R that is X->Y if and only if each X value in R associated with precisely one y value in R,R is then said to be functional dependency X->Y.

AB->C means A->C,B->C

C->D

D->A here all are candidate keys

the common subset of candiadate keys are super keys.

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