GATE Computer Science (CS) 2019 Solved Papers

Question : 6 of 65

Marks: +1, -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?

Validate

Solution:

Case I:

Criminals	P	Q	R	S
Assumption	F	T	F	F
Result	${Q}_{ {NC}}$	${S}_{ {c}}$	${R}_{ {C}}$	${Sc}$

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	${Q}_{ { C}}$	${S}_{ {NC}}$	${R}_{ { C}}$	${Sc}$

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	F
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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