Truth table to prove statements

Question

A, B and C. When questioned A says ''If B did not do it, then it was C." B says ''A and C did it together or C did it alone". C says ''We all did it together."

How would i be able to put these into an equation to use in truth table?

Any help at all would be great :)

Answer 1

Let $A$ denote "A did it."

Let $B$ denote "B did it."

Let $C$ denote "C did it."

A's claim: $\lnot B \rightarrow C$.

B's claim: $(A \land C) \lor C$

C's claim: $A \land B \land C$.

Can you see that we can make the case that two are telling the truth, and the third is telling a lie. Whose the sole liar?