An AI coach that shows where your CCAT points go.

No, that one is False. This is modus tollens.

If every waiter wore a uniform and Mark didn’t, Mark can’t be a waiter.

If A were true, the arrow would force B to be true. But you know B is false. So A cannot be true, and the claim “Mark was a waiter” is False.

Run the Uncertain test

• A true, B false: breaks A -> B. Not possible.
• A false, B false: A -> B still holds. Possible.

Only one version works, so the answer is forced: False.

Yes, Uncertain. Your reason is exactly right: A is one way to get B, but not necessarily the only way. Concluding A would be affirming the consequent, which is invalid.

“Is B true?” is still True. You were told it, so it is still known.

Yes, Uncertain. A is not the only possible cause of B, so A being false tells you nothing about B. Concluding !B would be denying the antecedent.

Rule: A -> B, plus one fact

Each row is one fact you are told. The columns show what that makes each claim.

Bold cells are the ones the test actually asks about: the letter you were not told.

Short form

• A -> B, A ⊢ B
• A -> B, !B ⊢ !A
• A -> B, B ⊢ nothing about A
• A -> B, !A ⊢ nothing about B

Related statements

The converse and inverse are the two traps in rows 3 and 4 of the first table. If you catch yourself using either, the answer is Uncertain.

Memory hook

Forward from a true front (A gives B). Backward from a false back (!B gives !A). Anything else: the other letter is Uncertain. The letter you were told is always still known.