Consider the following statements relating to the level of poker play of four…
2016
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
Answer: D. neither (i) nor (ii) — Given statements: P always beats Q. R always beats S. S loses to P only sometimes (so P does not always beat S). R always loses to Q (so Q always beats R).…
- A.
(i) only
- B.
(ii) only
- C.
(i) and (ii)
- D.
neither (i) nor (ii)
Attempted by 56 students.
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Correct answer: D
Given statements:
P always beats Q.
R always beats S.
S loses to P only sometimes (so P does not always beat S).
R always loses to Q (so Q always beats R).
Analysis:
From 'P always beats Q' and 'Q always beats R', we get that P always beats R by transitivity of the 'always beats' relation.
From 'R always beats S', combining with P always beats R gives P always beats S by transitivity.
However, the statement 'S loses to P only sometimes' explicitly says P does not always beat S, which directly contradicts the conclusion that P always beats S.
Because the premises lead to a contradiction, you cannot derive reliable logical conclusions from them about certainty of outcomes.
Conclusion:
Neither statement can be logically inferred. The set of premises is inconsistent, so you cannot validly conclude that P is guaranteed or even "likely" to beat all three, nor that S is the absolute worst player.
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