Reasoning :: Binary logic,Clock And Calenders :: Binary logic

• Binary logic,Clock And Calenders - Binary logic
• Binary logic,Clock And Calenders - Clock
• Binary logic,Clock And Calenders - Calenders

In a colony, each person is either a truth teller, who always speaks truth or a liar, who always lies or an alternator, who alternates between truth and lie in any order.When a question is asked to three persons P1,P2 and P3 whose names are P, Q, R not necessarily in the same order they replied in the following manner.

P1: I am Q.

      Exactly one of us is liar.

P2: Exactly one of us is truth teller

     P3 is P

P3:Exactly one of us is an alternator

     I am not R

If there is at least one truth teller, then who is R?

Answer:

Explanation:

Suppose, P1 is a truth-teller.As exactly one of them is a liar,  second statement of P2 or P3 must be false. But if the second statement of P2 is false, then P3's second statement must be false.

Therefore, P2's first statement is true.

Therefore, P3's first statement must be false .

Suppose P2 is a truthteller, then P3 is P.

Therefore, P3's second statement is true.

$\Rightarrow$ P3's first statement must be false

Therefore, P1 must be an alternator.

P1's second statement must be false

Therefore P1 is Q.

$\Rightarrow$P2 is R.

If P3's both the statements are true,which is not possible as it violates the conditions given by P2 and P1.

Three persons A,B, C were sitting in a row of three chairs.When asked about their respective positions, each of them made two statements as follows.It is known that each of them made a true statement and a false statement in any order.

A: I am at te extreme left.

    C is at the extreme right.

B: A is between me and C and myself.

    I am at extreme right.

C: I am at the extreme left.

    B is at the extreme right.

What are the actual positions from left to right?

Answer:

Explanation:

Assuming the first statement of A as true and second as false, we get

If the first statement of A is lie and second is true, then C will be at extreme right and A will be at centre and B will be at the extreme left.But it violates the conditions given by C.

Therefore the arrangement from left to right will be A-C-B.

While I was entering defence Headquaters , I met three persons Lau, Nau and Pau.One among them always speaks truth , one always lies and the other alternates between truth and lie in any order.At least one among them knew the access code for high security areas.When I asked them about the code, their replies were as given below.Each of them made two statements.

Lau:Only one among us knows the code.

      Pau knows the code.

Nau:I dont know the code.

      : Lau knows the code.

Pau:Each one among us knows the code.

     :I know the code.

Who among them knows the code?

Answer:

Explanation:

Assuming both the statements of Lau are true, we get Pau knows the code.So, the second statement of Pau is true and his first statement must be wrong .So, both statements of Nau must be false, but the first statement happens to be true.

Assumingg both the statements of Nau are true.

Assuming Pau's both the statement are true.Both the statements of Lau or Nau cant be false, it violates the given conditions.

Sa, Re and Ga participated in a race and each won d different medal among Gold,Silverand Bronze, not necessarily in that order.One among them always speaks truth, one always lies and one alternates among truth and lie in any order.When they were asked about the medals won by them ,the following were their replies.

Sa: I won the Gold medal.

       Re won the Bronze medal.

Re:I won the gold medal.

     Ga won the Bronze medal.

Ga:I won the Bronze medal.

     Sa won the gold medal.

Who among them won the Bronze medal?

Answer:

Explanation:

1.Assuming Sa always speaks truth.

$Sa\rightarrow Gold$, $Re\rightarrow Bronzee$, $Ga\rightarrow Silver$

2.Assuming Re always speaks truth:

Assuming Ga always speaks truth, the first statement of Sa and second statement of Re become true which violates the conditions.

From 1. Re won the Bronze medal.

From2.Ga won the Bronze medal.

So, it cannot be determined

In Honololo,Island , there are two types of people-truth tellers and liars. Truth-tellers always speak truth and liars always lie.I met three residents Ho,Lo, and Po, and asked them "who among you is the liar?"The Following are their replies.

Ho:I am a truth-teller.

Lo:Ho is not a truth-teller.

Po:Lois not a liar.

If it is known that exactly oneperson among them is a liar and the other two are truth-tellers,then who among them is the liar?

Answer:

Explanation:

First let us take the statements made by Lo and Po.If we assume that Lo is liar, then Po must be a liar.As we know that there is only one liar, Lo and Po cannot be the liars.

So, Ho must be the liar and Lo and Po are truth-tellers.

• Binary logic,Clock And Calenders - Binary logic
• Binary logic,Clock And Calenders - Clock
• Binary logic,Clock And Calenders - Calenders