Homework 3 Weijie Cai
1. R(A,B,C)withFD:C->AandA->B
a. C -> A, A -> B, C -> B (By transitivity in Armstrong¡¯s axioms) b. {C}
2. S(A,B,C,D)withFD:AB->C,BC->D,CD->A,AD->B
a. AB->C,BC->D,CD->A,AD->B
b. If order doesn¡¯t matter: {A,B,C}, {A,B,D}, {B,C,D}
If order matters: {ABC}, {ABD}, {BCA}, {BCD}, {CDB}, {DAB}
3. R(A,B,C,D,E)withFD:DE->C,B->D,ABE->C
a. DE->C,B->D,ABE->C
b. R_1 = R(A,B,D,E) R_2 = R(A,B,C,E)