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?
Logical Deduction: Identifying the Culprit
This problem involves identifying the criminal who committed the crime by analyzing the statements made by four suspects: P, Q, R, and S. The key constraints are:
- Exactly one of the four individuals committed the crime.
- Exactly one of the four statements made is true.
Analyzing the Statements
First, let's clarify each statement:
- P's Statement: "Q committed the crime."
- Q's Statement: "S committed the crime."
- R's Statement: "I did not do it." (Meaning R is innocent).
- S's Statement: "What Q said about me is false." Since Q said "S committed the crime", S's statement means "It is false that S committed the crime", or simply "S did not commit the crime."
Case-by-Case Analysis
We will assume each person committed the crime and check if the conditions hold true.
Case 1: Assume P committed the crime.
- P's Statement ("Q committed"): False.
- Q's Statement ("S committed"): False.
- R's Statement ("R did not commit"): True.
- S's Statement ("S did not commit"): True.
- Result: Two statements (R and S) are true. This contradicts the rule that only one statement is true.
Case 2: Assume Q committed the crime.
- P's Statement ("Q committed"): True.
- Q's Statement ("S committed"): False.
- R's Statement ("R did not commit"): True.
- S's Statement ("S did not commit"): True.
- Result: Three statements (P, R, and S) are true. This contradicts the rule.
Case 3: Assume R committed the crime.
- P's Statement ("Q committed"): False.
- Q's Statement ("S committed"): False.
- R's Statement ("R did not commit"): False (because R did commit).
- S's Statement ("S did not commit"): True (because R committed).
- Result: Exactly one statement (S) is true. This scenario fits both conditions perfectly.
Case 4: Assume S committed the crime.
- P's Statement ("Q committed"): False.
- Q's Statement ("S committed"): True.
- R's Statement ("R did not commit"): True.
- S's Statement ("S did not commit"): False (because S did commit).
- Result: Two statements (Q and R) are true. This contradicts the rule.
Conclusion
The only case that satisfies the condition of exactly one true statement is Case 3, where R is assumed to be the criminal. Therefore, R committed the crime.
Important Questions from Logical Deduction
- Consider the following two phonological rules:
Rule 1: Vowel Epenthesis of [ɪ] after sibilant-ending stems
Rule 2: Progressive Voicing Assimilation of the plural affix
Which ONE of the following rule ordering relations apply in the case of regular English pluralization as in ‘horse’ – ‘horses’? - Based only on the conversation below, identify the logically correct inference:
“Even if I had known that you were in the hospital, I would not have gone there to see you", Ramya told Josephine. Consider a five-digit number PQRST that has distinct digits P, Q, R, S and T, and satisfies the following conditions:
$P < Q$
$S > P > T$
$R < T$
If integers 1 through 5 are used to construct such a number, the value of P is:Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the complex revealed that all of those residents who are well established in their respective fields happen to be academicians. The survey also revealed that most of these academicians are authors of some best-selling books.
Based only on the information provided above, which one of the following statements can be logically inferred with certainty?- P, Q, and R talk about S's car collection. P states that S has at least 3 cars. Q believes that S has less than 3 cars. R indicates that to his knowledge, S has at least one car. Only one of P, Q and R is right. The number of cars owned by S is
