it is a problem of logic concerning who killed Julius Caesar.

I have written the logical sentences and build the truth table, but I cannot find a way to combine all these...

p: Marcus Antonius(says): Cassius or Brutus or both

q: Cassius(says): not me. Marcus Antonius is lying

r: Brutus(says): if I did it, then the other two are guilty also.

m: Marcus Antonius is guilty

c: Cassius is guilty

b: Brutus is guilty

A guilty person always lies.

A non-guilty person always tells the truth

p: c OR b OR (c AND b)

q: c’ AND m (because a guilty always lies)

r: b => (c AND m)

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But if anyone is guilty, then they must be lying and the innocent are truthful so we can blank out all the rows where there are two Ts or two Fs in someone's columns.Open in new window

This leaves three valid possible scenariosM did it

C and B did it

C did it

All three (and only these three) satisfy all the given conditions.