Truth teller and lie detector problems

The key idea of the truth teller identification in competitive exams is to test one's logical ability to answer questions and its usage is increasing day by day, It is the way to test your ability to identify the level truth or lie from many given inferences to draw some conclusion.From the given set of statements by few persons, has to draw a conclusion.

Truth teller, Lie Detector.   

Types of people in Truth teller and lie detector problems:

Liar : A person who always lie.

Truth Teller :A person who always says the truth.

Alternator: A person whose answers always alters in a step fashion(example: if he say 3 statements, his statements' truthness can be either T, F, T or F, T, F)

One more point to Note:

"I'm a Liar":

It looks soo simple but there is a lot in it,A liar cannot say this(because it is the truth) and a truth teller cannot say this(As it is a lie), only an Alternator can say this statement.

When we get the statements from multiple persons, we may not easily distinguish them ,the only way is to apply "Benefit of Doubt".

Benefit of Doubt : means assuming that the person is a truth teller and check other statements if no contradiction is emerged then the assumed assertion is true.

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Example 1:

Amar visited a city and asked two persons,  Rama and Krishna of whom one is a truth teller and other is a liar-in which direction Bombay was.

They replied as follows.

Rama: 

1. Krishna is a Liar.
2. Bombay is in the east.

Krishna:

1. I am not a liar.
2. Bombay is in west.

solution:

First give the Benefit of Doubt to any one of them,

Iam giving Benefit of Doubt to Rama,=>Statements by Rama are true.

Krishna is a Liar and Bombay is in west are true.

When we inference Krishna 's statement,

He says: I am not a liar. (Assuming this as False)

Bombay is in west(This could also be false as he is a liar).

We can Drag the solution is "EAST"

Next give the Benefit of Doubt to Krishna,=>Statements by Krishna are true.

I am not a liar, Bombay is in west are true.

when we inference Rama's statements,

He says: Krishna is a liar(Assuming this as False)

Bombay is in east(This could be false as he is a liar)

We can Drag the solution is "WEST".

Here we have two possible inferences which could be possible so we can derive solution "Bombay is either in East or in West .

Example 2:

There are three creeds - truth tellers, liars, alternators.A and B belong to different creed among the three.Their replies for "Who is the Engineer?" are as follows:

A:

1. I am not the Engineer.
2. I am a Liar.

B:

1. I am not the Engineer.
2. A is not an alternator.

solution:

By observing the rules, we can easily say that A is an Alternator(as a Truth teller or a Liar can't use the statement "I'm a Liar")(False statement)

so 1st satatement of A is a True statement(since alternator replies are complimentary each time)

A:

1. Iam not the Engineer (T)
2. I am a Liar(F)

A is an Alternator but B's second statement is "A is not an Alternator"

so B can be either Alternator or a liar.

As we can have only one from each creed, B cannot be an alternator.(With no contradiction)

B:

1. I am not the Engineer.(F)
2. A is not an alternator.(F)

Conclusion: B is a Liar, A is an Alternator.

so B is an Engineer.

If you have any queries or doubts, feel free to comment :)