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There are 3 people, A, B, C. Each person either only tells the truth (is truthfu

ID: 3142174 • Letter: T

Question

There are 3 people, A, B, C. Each person either only tells the truth (is truthful) or only tells lies (is not truthful), independently (that is A being truthful does not imply B is or is not truthful, etc.). They then say the statements:

A: “Exactly one of us is telling the truth.”

B: “We are all lying.”

C: “The other two are lying.”

What can you conclude about the identities about A, B, C? Are they liars or truthful? You should do this problem similar to the one in class with a truth-table considering each possibility and determining if it is viable.

Explanation / Answer

We add a symbol r to represent the statement "c is truthful".The truth table below begins with TTT and follows till FFF.

In the table,we mark the row where the truthvalues of p,q,r match the truth values of A,B,C respectively

We conclude that the possible situation is

p is true while q and r are false

Therefore,A is one only telling truth

Statement 1 Statement 2 Statement 3 p q r Exact;y one is truthful all are lying A and B are lying T T T F F F T T F F F F T F T F F F F T T F F F F T F T F F F F T T F T F F F F T T