Aptitude skill lesson
Deductive reasoning: skill lesson
Deductive reasoning is the disciplined application of rules you have been handed to a case you have been handed, stopping precisely where the rules run out. Where logical reasoning tests the machinery of inference, deductive items test restraint: they hand you a policy, a clue set or a specification and reward the candidate who reaches the one conclusion that is forced and declines the three that are merely plausible. It is the dominant construct in legal and policy admissions tests, critical-thinking style batteries with a cannot-say option, drone and aviation rule-knowledge screening, and any role where a written procedure has to be applied to an awkward real case. Practice stays on this device unless you export it.
Published · last reviewed
Applies to Novus Learn 0.1.0
What changed, and when
- , Replaced the body of all 27 non-judgement lessons with construct-specific material: six worked examples each, carrying the actual arithmetic, the actual inference or the actual procedure, plus expanded objectives, practice tips and glossary. Every 'Related Learn topics' link now points at a real page on this site rather than a generic search. The eight workplace-judgement lessons are unchanged.
- , Rebuilt the lesson page around a sticky contents rail, per-section links, previous/next lesson navigation, and two graded checkpoints drawn from the open practice bank.
- , Repaired the aptitude integrations behind the lessons so each one links to skill-specific practice instead of the unscoped fixture engine.
- , Published one lesson for each of the 35 aptitude skill constructs: objectives, worked examples, practice tips, glossary, Learn topic links, and sources.
These 35 skill lessons are authored and revised as one set, so they share one revision history rather than 35 identical dates.
Objectives
Copy link- Apply a multi-clause eligibility rule to a specific case and identify exactly which clause decides it, including when the case fails on one clause while satisfying every other.
- Distinguish validity from truth, and explain why an assessment item requires you to accept a premise you believe to be false.
- Choose the cannot-say or insufficient-information response correctly, and articulate the specific fact that would have been needed to decide.
- Solve a small elimination grid from a clue set, showing which clue eliminated which cell.
- Handle exclusive and inclusive or correctly, and know when eliminating one disjunct establishes the other.
- Derive a bounded answer from numeric constraints (a maximum, a minimum, or a short list of possibilities) rather than guessing a single value the constraints do not fix.
Checkpoint: does the idea land?
Copy linkBefore the worked examples, check that the objectives above actually landed.
Two questions from the open practice bank, answered here and scored on this device. Untimed, ungraded, and not added to your practice history, the full bank is where attempts are recorded.
Examples
Copy linkA three-clause rule and the case that fails on one
A dispatch policy: an order ships the same day if it is placed before 14:00 local time, AND every line on the order is in stock, AND the account is not on credit hold. Three cases. Case A is placed at 13:40, has one of four lines backordered, and the account is clear. Same-day? No. The word AND makes this a conjunction: all three clauses must hold, and one failure is fatal regardless of how comfortably the others pass. The reason candidates get this wrong is not logic, it is arithmetic instinct. Two out of three feels like a pass, and the 13:40 timestamp is written to feel like the clause the item is really about. Case B is placed at 14:00 exactly, fully in stock, no hold. Same-day? No, because before 14:00 excludes 14:00 itself. Boundary wording is deliberate in policy items; before, by, up to and no later than are four different lines. Case C is placed at 09:15, fully in stock, account on credit hold, and the customer has paid the invoice that caused the hold but the hold has not been lifted in the system. Same-day? No. The rule keys on the account being on hold, not on whether it deserves to be, and importing your judgement about what the policy is trying to achieve is the single most reliable way to fail this construct.
Valid but false, true but unjustified
All mammals lay eggs. A whale is a mammal. Therefore a whale lays eggs. The argument is VALID, the conclusion follows inescapably from the premises, and its first premise is false, so the argument is unsound and the conclusion is false. Validity is a property of the shape, soundness is validity plus true premises. Now the mirror image. Some birds cannot fly. A penguin is a bird. Therefore a penguin cannot fly. The conclusion is true, but the argument is invalid: some birds cannot fly leaves open which ones, so the premises do not force it. A true conclusion reached by an invalid route earns nothing. This matters practically because deductive assessment items routinely use premises that are false in the real world, all deliveries to the northern depot arrive by rail, precisely to test whether you reason from the page or from memory. The instruction to treat the statements as true is not a formality; a candidate who silently corrects a premise is answering a different question. Read the premise, accept it for the duration of the item, and put your world knowledge down.
When cannot say is the correct answer
Given: every technician on the night shift holds a confined-space ticket. Priya holds a confined-space ticket. Candidate conclusion: Priya works the night shift. The answer is cannot say, and the reason is worth naming precisely. The rule runs from night-shift technician to ticket-holder, and Priya has been placed at the ticket-holder end. Nothing in the premises says ticket-holders are exclusively night-shift technicians, so Priya could be a day-shift technician, a contractor or a safety officer. The fact that would have decided it is a converse or an exclusivity clause, only night-shift technicians hold the ticket, and being able to state that missing fact is the difference between guessing cannot-say and knowing it. Two calibration checks. First, cannot say is not a hedge for items you find hard; if you can construct one world where the conclusion is true and one where it is false while both satisfy every premise, cannot say is provably right. Second, cannot say is wrong whenever a contrapositive settles the matter: given the same premise and the fact that Sam does NOT hold a confined-space ticket, Sam definitely does not work the night shift, and answering cannot say there is a real error.
An elimination grid, solved clue by clue
Three analysts (Rowan, Sana, Theo) are each based in one of Cardiff, Dublin or Edinburgh and each covers one of energy, retail or transport. Clues: (1) the Dublin analyst covers retail; (2) Theo is not in Dublin and does not cover transport; (3) Sana is not based in Cardiff; (4) Rowan is not based in Edinburgh; (5) Sana does not cover transport. Work the cities first. Clues (2), (3) and (4) leave only two city arrangements: Rowan-Cardiff, Sana-Dublin, Theo-Edinburgh; or Rowan-Dublin, Sana-Edinburgh, Theo-Cardiff. Take the second. Rowan in Dublin covers retail by (1); Theo cannot cover transport by (2), so Theo covers energy; that leaves transport for Sana, which clue (5) forbids. The whole arrangement dies. So the first stands: Rowan in Cardiff, Sana in Dublin, Theo in Edinburgh. Now the subjects. Sana in Dublin covers retail by (1). Theo is not transport by (2), so Theo covers energy. Rowan takes transport, and clue (5) is satisfied because Sana has retail. Final grid: Rowan, Cardiff, transport; Sana, Dublin, retail; Theo, Edinburgh, energy. Two working habits do most of the lifting. Record negatives as well as positives. Theo-not-Dublin is as useful as any positive placement. And when a clue only bites after several others have landed, as clue (5) does here, park it and come back rather than abandoning the branch.
Or, and the two meanings it carries
A fault report states: either the sensor or the relay has failed, but not both. The relay tests good. Conclusion: the sensor failed. Valid, and comfortably so. The not both makes this an exclusive or, and eliminating one disjunct forces the other. Now strip the qualifier: either the sensor or the relay has failed. The relay tests good. Conclusion: the sensor failed. Still valid. Disjunctive syllogism works for the inclusive reading too, because inclusive or asserts at least one. The difference shows up on the OTHER side of the inference. With the exclusive version, learning the relay HAS failed tells you the sensor did not. With the inclusive version, learning the relay has failed tells you nothing at all about the sensor. Both may have gone. Candidates who treat every or as exclusive will confidently clear a good component; candidates who treat every or as inclusive will miss a genuine deduction. Read for the qualifier: but not both, exactly one of, and either-but-not signal exclusivity, while a bare or in a technical document is normally inclusive. When a policy says applicants must hold a degree or five years of experience, the inclusive reading is almost certainly intended, and an applicant with both is not disqualified.
Numeric constraints give you a bound, not a value
Four people share a 28-night on-call rota. Each person takes at least four nights. Ama takes exactly twice as many nights as Bo. Cal takes eight. What is the largest number of nights Ama can take? Set it up: A + B + C + D = 28 with C = 8 and A = 2B, so 2B + B + 8 + D = 28, giving 3B + D = 20. Both B and D must be at least four, so 3B is at most 16 and B is at most 5 (since B must be a whole number and 3 times 6 is already 18, leaving D = 2). B is also at least four, so B is 4 or 5. B = 4 gives A = 8 and D = 8: the rota is 8, 4, 8, 8, totalling 28, all at least four: legal. B = 5 gives A = 10 and D = 5: the rota is 10, 5, 8, 5, totalling 28: also legal. So the answer is 10. The trap answer is 12, produced by checking the total and forgetting that D would then be 2, below the floor. Two lessons live here. The constraints do not fix a single rota, and a candidate who insists on one answer for every person will invent a value; the honest output is a bound plus the small set of legal arrangements. And the binding constraint is the floor on D, not the total, identifying which constraint actually stops you going further is the entire skill in this item type.
Checkpoint: can you apply it?
Copy linkNow apply it. These come from a later section of the bank, so they are not more of the same.
Two questions from the open practice bank, answered here and scored on this device. Untimed, ungraded, and not added to your practice history, the full bank is where attempts are recorded.
Practice tips
Copy link- Before touching a rule-application item, list the clauses on separate lines and mark each one as satisfied, failed or unknown for the case in front of you. Conjunctions are decided by the first failure, and writing them out stops you from being led by the clause the item made most vivid.
- Circle every boundary word, before, by, at least, no later than, more than, up to and including. A large share of deductive marks turn on whether the boundary value itself is inside or outside the rule.
- When you reach for cannot say, write the one sentence that would have settled the item. If you cannot name that missing fact, you are probably guessing, and if you can, you are almost certainly right.
- Practise accepting false premises out loud. Say the premise is false in the real world and I am reasoning from it anyway before you answer; the habit protects you from the items that are deliberately built on untrue statements.
- On grid puzzles, record negatives in the grid, not just confirmations, and note which clue produced each elimination so you can retrace a branch instead of restarting it.
- Finish every numeric-constraint item by substituting your answer back into all constraints, including the ones you did not use. Attempts stay on this device, so the extra thirty seconds of checking costs nothing and catches the off-by-one that the answer options are designed to reward.
Glossary
Copy link- Valid argument
- An argument whose conclusion cannot be false while its premises are true. Validity is about structure alone and says nothing about whether the premises are actually correct.
- Sound argument
- A valid argument whose premises are also true. Assessment items test validity; soundness is usually outside the scope you are given.
- Premise
- A statement offered as given. In deductive items you are instructed to treat premises as true for the duration of the question, even where they contradict your own knowledge.
- Cannot say
- The response indicating that the premises are consistent with the conclusion being either true or false. It is a positive finding about the evidence, not an admission of uncertainty.
- Disjunctive syllogism
- The valid inference from either P or Q together with not-P to the conclusion Q. It holds for both the inclusive and the exclusive reading of or.
- Exclusive or
- A disjunction asserting that exactly one alternative holds, signalled by but not both or exactly one of. Unlike inclusive or, it also lets you infer not-Q from P.
- Counterexample
- A single case satisfying every premise while making the conclusion false. Producing one is the fastest proof that an argument is invalid or that an answer option is not forced.
- Binding constraint
- The constraint that actually stops a quantity going further. Naming it converts a vague numeric item into a definite maximum or minimum.
Sources
Copy link- Worked items written for Novus Learn from standard introductory logic and constraint reasoning: conjunctive rule application, validity versus soundness, disjunctive syllogism, and elimination grids. The grid and the rota problem were each solved exhaustively and checked for a unique answer.
- Terminology checked against the public Wikipedia articles 'Validity (logic)', 'Soundness', 'Disjunctive syllogism' and 'Exclusive or'. Definitions only; every case and clue set above is original.
- Novus Learn aptitude construct registry (catalog seed) for the construct scope and related suite mapping.
- Public educational framing only: not affiliated with any official exam board, publisher or employer, and no copyrighted test item is reproduced.
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