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GATE Computer Science (CS) 2019 Solved Papers
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© examsnet.com
Question : 6
Total: 65
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?
P
R
S
Q
Validate
Solution:
Case I:
Criminals
P
Q
R
S
Assumption
F
T
F
F
Result
Q
N
C
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
N
C
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
N
C
S
N
C
R
N
C
S
C
S
N
C
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
F
Result
Q
N
C
S
N
C
R
C
S
N
C
R is criminal in the result.
Hence this case satisfies only one person committed the crime.
© examsnet.com
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