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Consider the following statements relating to the level of poker play of four players P, Q, R and S.

I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q

Which of the following can be logically inferred from the above statements?

(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set

  • A.(i) only
  • B.(ii) only
  • C.(i) and (ii)
  • D.neither (i) nor (ii)

Answer: D

Neither can be inferred, so the answer is neither (i) nor (ii).

From the statements: P always beats Q, Q always beats R, and R always beats S. P beats S only sometimes, so S sometimes beats P.

(i) is not certain: P always beats Q, but nothing says P ever plays R or how often P beats R, and P loses to S part of the time, so 'likely to beat all three' is not established. (ii) is not certain either: S always loses to R, but S sometimes beats P, who always beats Q, so S is not simply the worst player. The chain of 'always' results is broken by statement III, which is the point of the question.

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