Gate2019 cs Q6

0. The 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?

Answer
Comment
Array

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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