“If” and “only if” in logical reasoning questions

Conditional reasoning becomes clearer when you write down what the rule guarantees and what it leaves open. Everyday expectations should not add conditions that the question never supplied.

Follow the arrow

Suppose the rule is: “If a card is a member card, it is blue.” Write this as member card → blue. A member card must be blue under the rule. A blue card does not have to be a member card, because other blue cards were not excluded.

If a card is not blue, you can conclude that it is not a member card: otherwise it would violate the rule. But a card that is not a member card may be blue or another colour. The rule does not settle that case.

Translate “only if” carefully

“Entry is allowed only if a pass is valid” makes a valid pass a necessary condition for allowed entry. In arrow form: allowed entry → valid pass. It does not say that every valid pass guarantees entry. There could be other requirements unless the problem rules them out.

By contrast, “If a pass is valid, entry is allowed” points from valid pass to allowed entry. The wording has changed the direction of the implication. Read the whole sentence before relying on familiar associations between its words.

Look for a counterexample

To test the claim “Every blue card is a member card,” imagine a blue visitor card. It obeys the original rule because the rule constrained member cards, not visitor cards. This counterexample shows that the stronger claim does not necessarily follow.

For practice questions, accept the stated premises as the puzzle's rules and distinguish “must be true” from “could be true.” If a conclusion is merely plausible, it has not met a must-be-true requirement. PickAQuiz's deductive questions include explanations so you can inspect that distinction after finishing the set.