Consider the relation Shipping(Ship, Capacity, Date, Cargo, Value) with the FDs: F = {ShipCapacity, ShipDateCargo, CargoCapacityValue}.

(a) Find a minimal basis for F.

(b) Suppose we decompose the relation Shipping into: R1(Ship,Capacity) and R2(Ship, Date, Cargo, Value). Is this decomposition lossless join and dependency-preserving? Why (not)?

(c) Answer the previous question if R is decomposed into the following 3 relations:

R1(Cargo, Capacity, Value),

R2(Ship, Capacity),

R3(Ship, Date, Cargo).