SOLUTION: Solve the problem using rules of inference and replacement: Premise 1) Q v (R . S) Premise 2) (Q > T) . (T > S) Conclusion /:S

    1:   Q or (R and S)
    2:   (Q -> T) and (T -> S)    |    S
    3:   Assume Q
         4:  Q -> T               2    Conjunction Elimination
         5:  T                    3,4  Modus Ponens
         6:  T -> S               2    Conjunction Elimination
         7:  S                    5,6  Modus Ponens

    8:   Assume ~Q
         9:  R and S              1,8  Disjunctive Syllogism
        10:  S                    9    Conjunction Elimination

   11:   :. S                     3-7,8-10 Law of Excluded Middle