Suppose we have relation r(a, b,c, d,e), with some set of fd'sand we wish to project those fd's onto relation s(a, b,c). give thefd's that hold in s if the fd's for r are:
a)ab--> de, c--> e, d--> c, and e--> a
b)a--> d, bd--> e, ac--> e and de--> b
c)ab--> d, ac--> e, bc--> d, d--> a and e--> b
d) a--> b , b--> c, c--> d, d--> e and e--> a

Write a program that performs a simple n-body simulation, called "jumping leprechauns." this simulation involves n leprechauns, numberd 1 to n. it maintains a gold value g_i for each leprechaun i, which begins with each leprechaun starting out with a million dollars worth of gold, that is, g_i = 1000000 for each i = 1,. in addition, the simulation also maintains, for each leprachaun, i, a place on the horizon, which is represented as a double-precision floating point number, x_i. in each iteration of the simulation, the simulation processes the leprachauns in order. processing a leprachaun i during its iteration begins by computing a new place on the horizon for i, which is determined by the assignment: