Gate2019 cs Q6

6The police arrested four criminals – P, Q, R and S. The criminals knew each other. They made the following statements:
P says “Q committed the crime.”
Q says “S committed the crime.”
R says “ I did not do it.”
S says “What Q said about me is false”.
Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime?

Option : B
Explanation : Case I:
Criminals P Q R S
Assumption F T F F
Result Q_NC S_C R_C S_C

S and R are criminal in the result is impossible because only one person committed the crime.
Case II:
Criminals P Q R S
Assumption T F F F
Result Q_C S_NC R_C S_C

Q and R are criminal in the result is impossible because only one person committed the crime.
Case III:
Criminals P Q R S
Assumption F F T F
Result Q_NC S_NC R_NC S_C

S_NC and S_C in the result which is contradiction. [S committed crime and same time not committed crime which is contradiction]
Case IV:
Criminals P Q R S
Assumption F F F T
Result Q_NC S_NC R_C S_NC

R is criminal in the result.
Hence this case satisfies only one person committed the crime.

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