Modus tollens: what you can validly infer from a conditional, a worked logical reasoning question

Worked solution

Correct answer: The alarm is not faulty

The principle

Modus tollens: from 'if P then Q' and 'not Q', we can validly infer 'not P'.

Steps

1. The rule is: faulty alarm (P) implies red flashing light (Q).
2. We are told the light is not flashing red, i.e. not Q.
3. If the alarm were faulty, the light would have to flash red (by the rule); since it does not, the alarm cannot be faulty.
4. Therefore the alarm is not faulty.

Heuristic to carry forward

Given 'if P then Q' and 'not Q', validly conclude 'not P' (modus tollens/contrapositive); never conclude from 'not P' alone.

Why each other answer is wrong

The light will flash a different colour

Introduces information about colour not supported by the rule, which only mentions red versus not-red.

The alarm is faulty

Directly contradicts the valid modus tollens conclusion.

No certain conclusion can be drawn about the alarm

Understates the certainty available; modus tollens does yield a certain conclusion here.