1)
i) S(A,B,C,D)
	A-->B, B-->C, B-->D
	
A+BCD == A-->BCD
B+CD  == B-->CD
C+
D+
AB+CD == AB-->CD
AC+BD == AC-->BD
AD+BC == AD-->BC
BC+D  == BC-->D
BD+C  == BD-->C
CD+
ABC+D == ABC-->D
ABD+C == ABD-->C
ACD+B == ACD-->B
BCD+
ABCD+

Keys: A

Superkeys: AB,AC,AD,ABC,ABD,ACD


ii) T(A,B,C,D)
	AB-->C, BC-->D, CD-->A, AD-->B

A+
B+
C+
D+
AB+CD == AB-->CD
AC+
AD+BC == AD-->BC
BC+AD == BC-->AD
BD+
CD+AB == CD-->AB
ABC+D == ABC-->D
ABD+C == ABD-->C
ACD+B == ACD-->B
BCD+A == BCD-->A
ABCD+


Keys: AB,AD,BC,CD

Superkeys: ABC,ABD,ACD,BCD


2)
c) R(A,B,C,D)
	AB-->C, BC-->D, CD-->A, AD-->B
	
A+
B+
C+
D+
AB+CD == AB-->CD
AC+
AD+BC == AD-->BC
BC+AD == BC-->AD
BD+
CD+
ABC+D == ABC-->D
ABD+C == ABD-->C
ACD+B == ACD-->B
BCD+A == BCD-->A
ABCD+

Keys: AB,AD,BC,CD

No violations.

d) R(A,B,C,D)
	A-->B, B-->C, C-->D, D-->A
	
A+BCD == A-->BCD
B+ACD == B-->ACD
C+ABD == C-->ABD
D+ABC == D-->ABC
AB+CD == AB-->CD
AC+BD == AC-->BD
AD+BC == AD-->BC
BC+AD == BC-->AD
BD+AC == BD-->AC
CD+AB == CD-->AB
ABC+D == ABC-->D
ABD+C == ABD-->C
ACD+B == ACD-->B
BCD+A == BCD-->A
ABCD+

Keys:
	A,B,C,D
	
No violations

e) R(A,B,C,D,E)
	AB-->C, DE-->C, B-->D

A+
B+D == B-->D
C+
D+
E+
AB+CD == AB-->CD
AC+
AD+
AE+
BC+D  == BC-->D
BD+
BE+CD == BE-->CD
CD+
CE+
DE+C  == DE-->C
ABC+D == ABC-->D
ABD+C == ABD-->C
ABE+CD ABE-->CD
ACD+
ACE+
ADE+C == ADE-->C
BCD+
BCE+D == BCE-->D
BDE+C == BDE-->C
CDE+B == CDE-->B
ABCD+ 
ABCE+D == ABCD-->D
ABDE+C == ABDE-->C
ACDE+
BCDE+
ABCDE

Keys:
	ABE, ABCD

BCNF:

B-->D
R1(B,D) (B-->D)
R2(A,B,C,E) (AB-->C, BE-->C, ABE-->C)

AB-->C
R21(A,B,C) (AB-->C)
R22(A,B,E) (none)