Consider a relation schema R = {M, N, P, Q, S} and its functional dependency set F = {N → Q,S → M,M →P,P → S}. Is MN a super key of R? Is MN a candidate key of R? (a) MN is not a super key for R; MN is not a candidate key for R. (b) MN is a super key for R; MN is not a candidate key for R. (c) MN is a super key for R; MN is a candidate key for R. (d) MN is not a super key for R; MN is a candidate key for R.

Consider the relation schema Appointment={Patient, GP, Date, Time, Clinic, Room} and the followingset Σ of FDs:• Patient, Clinic, Date → Time• Patient → GP• GP → Clinic• Clinic, Date, Time, Room → Patient• Patient, Date, Time → Clinic, RoomIs the above relation schema Appointment in BCNF? If not, identify a BCNF decomposition for Appointment. You need to include the main steps used for identifying the BCNF decomposition. Check ifthis BCNF decomposition is dependency preserving

Consider a relation schema R = {A, B, C, D, E} and its functional dependency set F = {A → B,CD → E,B →D,E → A}. Which ones of the following are not candidate keys for R? (a) A(b) BC(c) CD(d) D(e) E

1. Consider a relation schema R1(A, B, C, D) that satisfies the set of functional dependencies F1 ={A→B, B→C, C→A}.a) Calculate A + and (AC)+b) Can AB→ C? Justify your answer.c) Find all the candidate keys of R1 using F1 and show your steps to find them. 2. Consider a relation schema R2(A, B, C, D) that satisfies the set of functional dependencies F2 = {A→B, C→D, D→AC}.a) Is (AD) is candidate key of R2? Justify your answer.b) Is R2 in BCNF? Explain the reason to your answer.c) If R2 is not in BCNF, give a lossless-join BCNF decomposition of R2. Is this decomposition dependency preserving? 3. Consider a relation schema R3(A, B, C, D, E) that satisfies the set of functional dependencies F3 = {A → BC, AC → BD}.a) Calculate (AC)+ and (AE)+b) Is AB → C in F3 +? Justify your answer.c) Find the canonical cover Fc of F3.d) Is R3 in 3NF? Explain the reason to your answer. If R3 is not in 3NF, give a lossless-join, dependency preserving 3NF decomposition of R3.