Consider Subscript C as criminal, NC as not criminal.
Case I: Consider P as True
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 also $S_{NC}$ and $S_C $ in the result which is a contradiction. [S committed the crime and same time not committed crime which is contradiction]
Case II: Consider Q as True
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 III: Consider R as True
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 a contradiction. [S committed a crime and same time not committed crime which is contradiction]
Case III: Consider S as True
Criminals |
P |
Q |
R |
S |
Assumption |
F |
F |
F |
T |
Result |
$Q_{NC}$ |
$S_{NC}$ |
$R_C$ |
$S_{NC}$ |
R is a criminal in the result. Hence this case satisfies only one person committed the crime.
Therefore R Committed the crime which is option B in Question