deductive-reasoning-s01-q01
A statement about every member of a group applies to each individual member. Membership in the group plus the universal rule settles the case immediately.
This is untimed educational practice for one cognitive skill. It is not a clinical, diagnostic, employment, or professionally recognized assessment, and it does not produce an IQ score or credential.
A statement about every member of a group applies to each individual member. Membership in the group plus the universal rule settles the case immediately.
Two universal statements link end to end: everything in the first group belongs to the second, and everything in the second has the sticker. Follow the chain in the direction it is stated.
The statement says where the top-shelf novels sit in the wider category of hardbacks, not that the category holds nothing else. Reversing a universal statement like this is the classic converse error.
Two groups sharing a feature need not overlap each other. A shared middle term establishes no direct link between the groups on either side of it.
The second statement tells you that tray 4 holds packet R seeds and nothing else, so the universal claim about packet R covers every seed in the tray.
If every member of a group has a feature, then anything lacking that feature cannot be a member. This backwards form of a universal statement is always available to you.
A recipe in both chapters would have to use butter and not use butter at once. Since that is impossible, the two chapters can share no recipe.
A universal rule only reaches an individual once that individual is placed inside the group. The missing statement is the one that puts Ivo in the group the rule describes.
"All" distributes across every member of the group without exception, so the count simply tells you how many individual cases the rule covers.
The chain runs one way: quartet membership leads to a stringed instrument, which leads to a locker. Arriving at the end of a chain never lets you travel back up it.
A "no" statement excludes a feature from an entire group, so anyone who has that feature must sit outside the group.
Two "some" statements about the same collection may describe the very same boxes or entirely separate ones. Neither overlap nor separation can be established from them alone.
Denying a universal claim needs only a single exception. "Not all" is therefore much weaker than "none", and says nothing about how many chairs stack.
The collection definitely contains nocturnal animals, and no reptile there is nocturnal, so those particular animals must fall outside the reptile group.
The first-aid trained volunteers definitely exist, and the second statement rules every first-aid trained person out of the night shift, so those volunteers are excluded from it too.
The airport vans sit wholly inside the fleet, so an exclusion that applies to the whole fleet applies to them. What they do run on is never stated.
A "some" statement guarantees that at least one such cheese exists, and the universal rule then applies to it. The conclusion inherits the weaker quantifier of the two.
Since being unsigned and being filed never occur together, a filed form cannot be an unsigned one. Identifying the excluded combination is the whole of the work here.
A universal claim and the statement that it has an exception are direct contradictories: exactly one of them holds, whichever way the shelf actually looks.
The exclusion means no single item can be both a sample and for sale, so the two groups described on that table must be made up of different items.
When the condition of an if-then statement is confirmed, its result follows immediately. This is the most direct use a conditional has.
If the condition would guarantee the result, then the absence of the result rules the condition out. Ruling out backwards is always valid; confirming backwards is not.
Take the statement as given: a rise above the threshold would have produced an alert, so no alert means no such rise. How far below the threshold it stayed is never stated.
The condition is satisfied, so the stated result follows. Note also that the conditional describes a rule, not a cause running the other way.
Once the conditional is granted, an absent result leaves no room for the condition to hold. Doubts about the equipment would question a premise rather than the reasoning built on it.
The condition of the rule was met, so its requirement applies to her. A rule tells you what is required, not whether the requirement was actually met.
The statement gives one route to the one o'clock opening, not the only route. Working backwards from a result to its stated condition is not a valid move.
The rule states what a high score guarantees, not what a lower score rules out. Other routes to an interview are neither offered nor excluded.
A conditional applies afresh to every occasion on which its condition holds, so two bookings produce two unlockings.
No case number means no panel review, and no panel review means the claim was not late. A denial travels backwards along a chain of conditionals one link at a time.
The statement names one thing that produces a pressure drop; it does not claim to name them all. Observing the result leaves the condition genuinely open.
A conditional promises what happens when its condition holds and says nothing about when it fails. She might have arrived early by some other route.
The premise rules out a jam without a stall, but permits a stall without a jam. Naming the other possible explanations is the quickest way to expose this pattern.
Removing the condition removes only the guarantee, not the possibility. Other flowerless plants could exist without contradicting anything given.
This is the one backwards move that does work: an arming would have produced the light, so a missing light rules the arming out.
Only a pair that confirms the condition of a conditional delivers its result. Pairs that confirm or deny the result lead either nowhere or to the opposite conclusion.
The rule obliges heavy lorries to use the bypass but does not forbid lighter ones from using it, so the route taken reveals nothing about the weight.
The absent result is what does the work here: a fault would have produced drift, so steadiness excludes the fault. Naming the pattern helps you reuse it.
A second route to the same result leaves the original statement intact while destroying the backwards inference. Looking for an alternative route is the standard test for this trap.
To attack an inference rather than a premise, look for a case where the premise still holds but the conclusion fails: here, a punctual northern delivery.
When at least one of two alternatives must hold and one is ruled out, the other is left standing.
Confirming one branch of an inclusive alternative tells you nothing about the other. Only ruling a branch out is informative.
"Exactly one" makes the alternatives exclusive, so confirming either branch rules the other out, which an ordinary "or" would not do.
"Neither" denies both alternatives at once, so it behaves as two separate negative statements joined together.
Eliminating one alternative in a statement that guarantees at least one leaves the remaining alternative established.
To deny that at least one alternative holds, you must deny every alternative. Denying a single branch leaves the original claim perfectly possible.
With the list of possibilities declared complete, striking off all but one leaves that one certain. This is elimination in its plainest form.
Allowing both branches to hold does not weaken elimination: at least one must hold, so ruling one out establishes the other.
The phrase "but not both" makes the options exclusive, so taking one closes off the other.
Eliminating the first branch forces the second, which the reply count then contradicts. When elimination leads to a clash, the set of statements is inconsistent.
A requirement states what you must have, not what is enough on its own. Meeting it clears one hurdle and leaves any others unmentioned.
A necessary condition works powerfully in the negative direction: without it, the outcome is ruled out entirely.
A guarantee is a sufficient condition: having it settles the outcome, while other routes to the same outcome remain possible.
"Cannot without" is the standard wording for a requirement. It blocks entry when the card is missing but promises nothing when the card is present.
When several conditions are all required, failing any one of them blocks the outcome, however many of the others are satisfied.
A sufficient condition guarantees the outcome but does not monopolise it, so seeing the outcome leaves that condition open.
Denying a requirement built from two parts denies at least one part, not necessarily both. Take care to keep the conclusion as weak as the evidence.
"Only to" marks a requirement rather than a promise, so satisfying it merely keeps the application alive.
When a condition is stated as the only requirement, it is both necessary and sufficient, so meeting it settles the outcome.
Calling a condition both necessary and sufficient closes off every alternative route: admission happens exactly when the two recommendations are in place.
"Only" introduces a requirement, so the action implies the badge. Reading it as a promise about all badge holders is the usual slip.
An "only" statement flips into if-then form with the borrowing as the condition and the membership as the result, which is the reverse of what the surface wording suggests.
"Unless" names the one stated exception, so with the exception absent the main statement holds.
Read the statement as "if the pitch is not waterlogged, the match goes ahead", then deny the result: the match not going ahead forces the exception to have applied.
The statement means that being forwarded implies being complete, so a completed application might still be held back for some unstated reason.
When "every" comes before "an", each member of the first group gets its own instance of the second. The stronger reading, with one adult shared by all, would need different wording.
The wording lets each reviewer choose a different chapter, so it supports only the per-reviewer reading and leaves whole chapters possibly unread.
"Only if" states a requirement for the payment, so the payment happening means the requirement was met.
"Only when" makes the volunteer a requirement, and a missing requirement rules the opening out.
The first notice makes a ticket necessary and the second makes it sufficient. Lacking the ticket, it is the necessary half that decides the case.
Comparisons of this kind chain together, so ahead-of relations line the three up in a single order with one runner at each end.
Both comparisons point away from the same box, which fixes that box at the bottom while leaving the other two unranked against each other.
Sketch the three positions on one line from the statements; the place that nothing lies south of sits at the southern end.
Assemble the statements into one chain running from the shortest upwards; the person nobody is said to exceed stands at the top.
"Immediately to the left" fixes exact neighbours, so the four shops fall into one fixed arrangement that can simply be read off.
Each statement adds one link, and here the links join into a single unbroken chain from the highest scorer down to the lowest.
Two items can be compared only when a path of statements runs between them. Here one pair has no such path, because each is linked only downwards to the thinnest folder.
Fill the stack from the fixed ends inwards: the bottom two and the top two positions are all pinned down, so the one remaining parcel takes the only free place.
The chain runs strictly downwards in age, so any claim that reverses the two ends contradicts it. Asking which statement must be false is the mirror of asking which must be true.
The ledger's fixed place and the two left-of statements confine the atlas and diary to positions two to four; the one-book gap then leaves a single arrangement standing.
Once one role is claimed by someone else, the remaining person's exclusion leaves only one role open to them.
Start with the clue that fixes a position outright, then apply the exclusion; the last drink falls into the only place left for it.
The two fixed desks leave only two free, and the neighbour restriction rules one of them out for Lena, which settles the other person by elimination.
When one person is excluded from all but one dish, that dish is theirs, whatever the other clues say.
Two subjects are assigned outright, and the double exclusion pins the third student to the one subject left for them, leaving the last subject for the remaining student.
Test the days the book could take: only one leaves room for the following day's delivery, and the remaining parcel then takes Monday.
Two placements for the middle pair survive the early clues, and the final exclusion knocks one of them out, fixing every flat.
The adjacency clue allows only two orders, and the clue about the last slot rules one of them out.
With both ends fixed, the adjacent pair can occupy the middle three places in two ways, and the restriction on the second place eliminates one of them.
The April traveller cannot be the one going to Malmö, and the clue about May rules out the second possible arrangement, leaving one complete grid.
Confirming the first condition triggers the first result, which is the condition of the second statement, so the chain carries you to its far end.
Work backwards one link at a time: no email means no return, and no return means the form was not incomplete.
Chains transmit confirmation forwards and denial backwards only. Confirming the end of a chain leaves everything earlier in it open.
Validity asks only whether the conclusion would have to follow if the statements were granted. Whether those statements are actually true is a separate question about soundness.
Valid reasoning can never carry you from true premises to a false conclusion, so this combination is itself proof that the reasoning is faulty.
A dry floor rules out the overflow, and no overflow rules out the running tap. Denial travels the length of a chain in the reverse direction.
Linked conditionals combine into a single conditional running from the first condition to the last result. Nothing about which statements actually hold can be drawn from rules alone.
Each backwards step removes one more link: the unfilled car park rules out the coach, and the absent coach rules out the cancellation.
Reasoning is judged by whether the conclusion is forced, not by whether it happens to be correct. A lucky hit leaves the backwards step just as invalid as before.
Starting from the unsigned log sheet, each rule is denied in turn back along the chain, and the last denial reaches the kiln at its head.