Let F(x): R -> Z be the floor function and C(x): R -> Z be the ceiling function. Select which of the following function equations are true (select zero or more answers).
a. C(x) - F(x) = 1 for all x.
b. C(F(x)) = F(x) for all x
c. C(F(x)) = F(C(x)) - 1 for all x
d. F(F(x)) = F(x) for all x