# Solve this hard Deduction Problem?

Jimmy claims that either Michelle or Toni tells the truth. Toni says that either Michelle or Jimmy tells the truth. Michelle says that neither Toni nor Jimmy tells the truth. Who, if anyone, is truthful?

### 3 Answers

- All hatLv 72 months ago
Since all three statements are "claims" only, we can't rely on any of them being true, so we can't know in this case who, if anyone, is being truthful.

- GuantanamoGeorgeLv 72 months ago
Suppose Jimmy is lying. Then Michelle must be lying, else Jimmy's claim is true. But Michelle says Jimmy is lying, which is true, so she isn't lying. So assuming that Jimmy is lying leads to a contradiction.

Suppose Jimmy is telling the truth. Then Toni is telling the truth and Michelle is lying, which does not contradict Jimmy's claim. That works.

- hayharbrLv 72 months ago
Jimmy tells truth (he said Toni tells truth and Michelle lies)

Toni tells truth (she said Jimmy tells truth and Michelle lies)

Michelle lies (since she said neither above tells truth)