for (i), we want all the x's in the domain of p(x) for which

for (ii) we want all the x's in the domain of p(x) AND q(x) (at the same time) for which

for (iii) we want all the x's in the range of q(x) that are in the domain of r(x)

for (iv) we want all the x's in the range of p(x) that are in the domain of s(x) and of course, we cannot have s(p(x)) = 0