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 \(\mathrm{P}=\{1,2\}, \mathrm{Q}=\{4,5\}\), \(R=\{2,3\}\), and \(S=\{3,4,5\}\), express each of the following symbolically by listing its elements and also in words.

(a) \(P \cup R\)

(b) \(P \cap R\)

(c) \(\bar{Q} \cup \bar{S}\)

(d) \(\bar{P}\)