Logical Reasoning Question:
Police had arrested four criminals P, Q, R and S.
→ P says Q committed crime
→ Q says S committed crime
→ R says “I didn’t do it”
→ S says what Q said about me is false.
There is only one criminal and also only one of the above statements is correct. Who among the four committed the crime? Also provide suitable explanation in support of your answer.
Answers
Given Question
Police had arrested four criminals P, Q, R and S.
→ P says Q committed crime
→ Q says S committed crime
→ R says “I didn’t do it”
→ S says what Q said about me is false.
There is only one criminal and also only one of the above statements is correct. Who among the four committed the crime?
Correct AnsWer
We Know that only one person committed the crime and only one given statement is correct.
Let's We Observe the Statements of P, Q, R and S :-
☆ When P is correct and Q, R, S are false :
Q committed crime, S did not commit crime, R committed crime, S committed crime. This situation is impossible.
☆ When Q is correct and P, R, S are false :
Q did not commit crime, S committed crime, R committed crime, S committed crime. This situation is impossible.
☆ When R is correct and P, Q, S are false :
it implies, Q did not commit crime, S did not commit crime, R did not commit crime, S committed crime.This situation is impossible.
☆ When S is correct and P, Q, R are false :
Q did not commit crime, S did not commit crime, R committed crime, S did not commit crime.
So, This situation is possible means R has committed crime.
Hence , option B is correct.
Note :- We know, this question is very logical and Also this is difficult to say that who committed the crime but According to logic , "R" is Committed for Crime. We Also know that Logic questions are solved by our thinking Sense. So, there are many thinkers Who gave their answers by according to Different Reasons. I hope you understand dear user. Thanks :)
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Given :
Police had arrested four criminals P, Q, R and S.
→ P says Q committed crime
→ Q says S committed crime
→ R says “I didn’t do it”
→ S says what Q said about me is false.
There is only one criminal and also only one of the above statements is correct.
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To Find :
Who among the four committed the crime? Also provide suitable explanation in support of your answer.
Solution :
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1 — Method :—»
A Long But Easy Method would be to Assume Each Statement True one by one and see if they fit the condition or cause any contradiction.
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- if P is saying Truth
it means Logically that everyone else is lying and Q commited the crime. Now Q,R,S are saying false so the opposite of their statements can be considered true.
Q's lie ⟹ S is not the Criminal
R's lie ⟹ R {himself} is the Criminal
S's lie ⟹ Q said Truth
Now, R's and S's statement both cause contradiction with our assumption so, our assumption must be wrong.
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- if Q is saying Truth
it means Logically that everyone else is lying and S commited the crime. Now Q,R,S are saying false so the opposite of their statements can be considered true.
P's lie ⟹ Q is not the Criminal
R's lie ⟹ R {himself} is the Criminal
S's lie ⟹ Q said Truth
Now, R's statement causes contradiction as if he is lied then He must be the Criminal but our assumption led S to be criminal. So, our assumption must be wrong.
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- if R is saying Truth
it means Logically that everyone else is lying and R is not the Criminal so it must be P,Q or S. Now P,Q,S are saying false so the opposite of their statements can be considered true.
P's lie ⟹ Q is not the Criminal
Q's lie ⟹ S is not the Criminal
S's lie ⟹ Q said Truth.
Now, S's statement causes contradiction as our assumption led to assuming that Q lied but if S also lied then Q must be saying the truth. So, our assumption must be wrong.
We, can stop here if we want as None of them was saying the truth So S must be saying the Truth. Which will Lead us That R is the Criminal
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- if S is saying the Truth
it means Logically that everyone else is lying and Q is telling False too{which was already assumed as others' must be lying}. Now P,Q,R are saying false so the opposite of their statements can be considered true.
P's lie ⟹ Q is not the Criminal
Q's lie ⟹ S is not the Criminal
R's lie ⟹ R{himself} is the Criminal
This Condition agrees with both condition that one person i.e R is criminal and only one person is telling the truth i.e S.
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2 — Method :—»
Short-er But will req. a little brain processing in the start.
There is only one criminal and also only one of the above statements is correct.
→ P says Q committed crime
→ Q says S committed crime
→ R says “I didn’t do it”
→ S says what Q said about me is false.
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these Could be grouped as P & Q ; R ; S
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→ P says Q committed crime
→ Q says S committed crime
These can't be true as they will imply that Q or S, Respectively is the Criminal but R will contradict this as if he is lying he must be the Criminal...
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→ R says “I didn’t do it"
This can't be true as By seeing the question we can easily get to know that : {P and S collectively contradicts this}
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P ⟹ S
S ⟹ S' {S compliment......S-not}
So, Either of these must be true
Yes, we could've also jumped directly to this point.
→ S says what Q said about me is false.
This is the only One left So, this must be true.
it's justification has already been done above