If stores experience a decrease in revenues (p) then either attitudes have changed (q) or prices have risen (r).
(1) p -> q v r (2)~(q ^ r) -> ~ p
If attitudes have changed (q) then we have something to celebrate (s) (2) q -> s (3) ~s -> ~q
If prices have risen (r) then salaries have not kept pace (t)
(4) r->t (5) ~t- > ~r
The question asks us if salaries have kept pace (~t), which of the following must be true?
We can see from (5) that ~t -> ~r, if salaries have kept pace, the prices have not risen beyond what people can afford (C). We cannot infer ~p from ~q because a contrapositive of the original condition:
p - > q v r is ~q ^ ~r -> ~p
It means that both must be true - prices have not risen and attitudes have not changed - for us to conclude that stores will experience no sales decrease. Since we only know that one of these conditions is true - prices have not risen, we cannot infer that the other antecedent (~q), attitudes have not changed, is true, or that the consequent (~p), no sales decrease, is true. Since the rules of inference do not allow us to reach this conclusion, (D) is incorrect.
