Exercise 3.2.1 Consider a relation with schema R(A,B,C,D)and FD' sAB→C,C→D and D→A a)What are all the nontrieval FD's that follow from the given FD's?you should restrict yourself to FD's with single attributes on the right side. b)What are all the keys of R? c)What are all the superkeys for R that are not keys? Solutions: a)Nontrivial FD's (Implied FD's) Given FD's:AB→C,C→D,D→A A+=A,B+=B,C+={C,D,A},D+={D,A} AB+=(A,B,C,D),AC+=(A,C,,D),AD+=(A,D), BC+=(B,C,D,A),BD+={B,D,A,C),CD+=(C,D,A) ABC+=ABD+=BCD+=(B,C,D,A}ACD+=(ACD) Answer is: C->A,AB->D,AC->D,BC->A,BC->D,BD->A,BD->C, CD->A,ABC->D,ABD->C,and BCD->A. b)AB,BC,and BD are keys c)ABC,ABD,BCD,and ABCDExercise 3.2.1 Consider a relation with schema R(A,B,C,D) and FD’ s ABC, CD and DA a) What are all the nontrieval FD’ s that follow from the given FD’ s? you should restrict yourself to FD’s with single attributes on the right side. b) What are all the keys of R? c) What are all the superkeys for R that are not keys? Solutions: a) Nontrivial FD’ s (Implied FD’ s) Given FD’ s: ABC, CD, DA A+=A, B+=B,C+={C,D,A},D+={D,A} AB+={A,B,C,D},AC+={A,C,,D},AD+={A,D}, BC+={B,C,D,A},BD+={B,D,A,C},CD+={C,D,A} ABC+= ABD+=BCD+={B,C,D,A} ACD+={ACD} Answer is: C->A, AB->D, AC->D, BC->A, BC->D, BD->A, BD->C, CD->A, ABC->D, ABD->C, and BCD->A. b) AB, BC, and BD are keys c) ABC, ABD, BCD, and ABCD