# GATE | GATE-CS-2016 (Set 1) | Question 8

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)

Explanation: All three can Beat S, but S loses to P only sometimes. So, (ii) can not be inferred from the given statements.

Defeating in Poker is not transitive. P beats Q. Q beats R and R beats S. Yet S loses to P only sometimes, meaning that S mostly wins against P. So we can not logically infer that P is likely to beat R.

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