Deductive reasoning: guide and free practice

Separate certainty from possibility

Could be true means at least one valid arrangement supports the claim. Must be true means every valid arrangement supports it. Do not choose a statement merely because it describes one neat arrangement you found.

Translate conditions carefully

If A then B permits both A and B, and it permits B without A. It does not permit A without B. You may infer not A from not B, but you may not infer A simply from B. The word only often reverses the direction people expect: only managers approve refunds means approval requires being a manager.

Test the conclusion with a counterexample

1. Write the rules in short form.
2. Assume the proposed conclusion is false.
3. Try to satisfy all the original rules anyway.
4. If you succeed, the conclusion was not necessary.

Ordering and scheduling

For schedules, identify fixed positions and precedence constraints before trying whole sequences. Unless stated, before does not mean immediately before. Our practice mixes conditional rules, ordering, eligibility and small numerical constraints. Explanations show the precise rule that rules out the other interpretations.

Prerequisites and practice levels

First distinguish before from immediately before, exactly one from at least one, and necessary from sufficient. Foundation questions isolate one rule. Intermediate questions combine adjacent scheduling blocks and access conditions. Advanced questions chain project exclusions and limited selections. Five questions share each scenario in the added sets; use only its explicit rules.

Worked example: an adjacent block

Four tasks P, Q, R and S occur once each. P is immediately before R and Q is last. Treat P R as one block. S P R Q and P R S Q both work. P is before Q in every arrangement, but P is not necessarily first. A single valid schedule disproves “must be first”; it cannot prove that all schedules start with P.

Worked example: conditions in the right direction

If approval requires a check and approval issues a pass, approval implies both check and pass. No pass rules out approval. Having a pass does not prove approval when passes may be issued for other reasons. A completed check does not guarantee approval unless the rule explicitly makes it sufficient.

A complete constraint method

1. Write each allowed person, slot or proposal once.
2. Apply fixed exclusions and adjacent blocks.
3. Apply the question’s extra condition without carrying conditions over from earlier questions.
4. For must, seek a counterexample; for could, construct a valid example; for impossible, eliminate every valid arrangement.
5. Check that the extra condition is feasible unless the question explicitly asks about inconsistency.

Common mistakes and next steps

Do not assume an empty category has members, reverse an implication, or choose an attractive arrangement without checking all rules. On review, write a counterexample for each tempting distractor. Progress after you can explain the forced chain. Continue to critical thinking for real-world assumptions and scheduling practice for further ordering constraints.

Your first practice session

Treat all premises as true. Select the one conclusion or arrangement required by the supplied rules; use no outside assumptions.

Try 10 questions with explanations

Choose your practice difficulty

Difficulty labels describe the steps needed in these teaching sets; they are not validated ability bands. Start with foundation practice and move on after you can explain your method.

• Foundation: 10 questions — single conditions, simple orderings and necessary conclusions.
• Intermediate: 10 questions — Combine scheduling blocks and necessary conditions in two original scenarios.
• Advanced: 10 questions — Chain project assignments and constrained selections in two original scenarios.

Continue learning

• Critical thinking
• Inductive reasoning
• Verbal reasoning

About this practice

These are independently written teaching questions. A practice score helps you review your answers; it is not a validated hiring prediction or an official employer score.