The police arrested four criminals – P, Q, R and S. The criminals knew each other. They made the following statements
Q. 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?
(A) P
(B) R
(C) S
(D) Q
Ans: R
Solution:
Suffix C as criminal, NC as not criminal.
Case I:
| Criminals | P | Q | R | S |
| Assumption | T | F | F | F |
| Result | QC | SNC | RC | SC |
Q and R are criminal in the result is impossible because only one person committed the crime.
Case II:
| Criminals | P | Q | R | S |
| Assumption | F | T | F | F |
| Result | QNC | SC | RC | SC |
S 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 | QNC | SNC | RNC | SC |
SNC and SC 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 | QNC | SNC | RC | SNC |
R is criminal in the result.
Hence, this case satisfies only one person committed the crime.