GATE CS 2016 Set 1 — Question 8
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Question
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 QWhich 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
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to QWhich 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
Correct answer
(D) neither (i) nor (ii)
Solution
From the statements:
However, statement III says loses to only sometimes. This contradicts a strict transitive hierarchy where would always beat . Since can beat or draw with (the top player in the chain), is not the "absolute worst" player (refuting ii). Similarly, since does not always beat , we cannot infer is likely to beat all three other players consistently, especially given the non-transitive nature introduced by statement III. Thus, neither inference is logically sound based strictly on the provided statements.
1.
2.
3. loses to only sometimes (implies wins or draws against sometimes)
4. (since always loses to )
Combining the definite relationships: .However, statement III says loses to only sometimes. This contradicts a strict transitive hierarchy where would always beat . Since can beat or draw with (the top player in the chain), is not the "absolute worst" player (refuting ii). Similarly, since does not always beat , we cannot infer is likely to beat all three other players consistently, especially given the non-transitive nature introduced by statement III. Thus, neither inference is logically sound based strictly on the provided statements.
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