3.5 To construct sample spaces for experiments in which we deal with non-numerical data, we often code the various alternatives by assigning them numbers. For instance, if an engineer is asked to rate the performance of a new machine with respect to its replacement as poor, not satisfactory, no change, satisfactory, or excellent, we might assign these alternatives the codes, 1, 2, 3, 4, and 5. If P = {1, 2}, Q = {4, 5}, R = {2, 3}, and S = {3, 4, 5}, express each of the following symbolically by listing its elements and also in words.

(a) P ∪ R

(b) P ∩ R

(c) Q ∪ S

(d) P