logical-reasoning-s01-q01
When the 'if' half of a rule is satisfied, the 'then' half must follow. Confirming the condition is the most direct way to apply a conditional.
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When the 'if' half of a rule is satisfied, the 'then' half must follow. Confirming the condition is the most direct way to apply a conditional.
A weight of 3.4 kg satisfies the stated condition, so the labelling requirement applies to this parcel. The rule says nothing at all about what lighter parcels carry.
A conditional guarantees only that the stated condition brings the stated result, every time. It leaves open whether other causes produce that same result.
Ruling out the condition does not rule out the result, because Ravi may leave early for some other reason. This tempting mistake is called denying the antecedent.
This is valid modus tollens: if P implies Q, and Q is false, then P must be false.
A lapsed subscription would guarantee a dead card, so a working card rules the lapse out. Denying the result of a rule lets you deny its condition.
An overnight stay would have required a lamp; since no lamp is displayed and the rule was followed, that overnight stay cannot have happened.
The rule promises an amber light when toner runs out, but never claims toner is the only trigger. A result cannot be traced back to one cause unless the rule rules the alternatives out.
Adding the fact that no other route to the result exists makes the rule work in both directions, so the result can now be traced back to its only possible cause.
Refunds are promised for cancellations, but the rule does not make cancellation the only ground for a refund. Working backwards from a result is safe only when the rule closes off the other routes to it.
We only know engineers hold the certification. Not that Priya is an engineer, or that only engineers can hold it. Her role isn't stated.
An 'all' statement applies to every member of the group without exception, so anything identified as a harbour tour inherits the rule.
A 'no' statement excludes every member of the group, so anything shown to belong to that group inherits the exclusion.
In logic 'some' means at least one and leaves the rest of the group open. Everyday speech hints that 'some' excludes 'all', but the statement itself makes no such promise.
This is a valid categorical syllogism: if no A are B, and all C are A, then no C are B.
Every flat in the block has a balcony, so any subgroup of those flats has balconies too. Naming a subgroup never creates an exception to an 'all' statement.
Belonging to the excluded group would make Sunday work impossible, so someone who does work Sundays cannot belong to it.
Chain the two statements: the hotel's delegates all fall inside the coach group, and that whole group is excluded from arriving early, so the smaller group inherits the exclusion.
Sharing a property does not make two groups overlap, coincide, or exclude one another; all that follows is the shared property itself. Reading more into it is the undistributed-middle mistake.
Green tags belong only to serviced machines, so anything unserviced cannot carry one. 'Some are not serviced' guarantees at least one such machine exists.
'Must have' marks payment as necessary rather than sufficient. Meeting a necessary condition clears one hurdle and leaves any others standing.
A necessary condition works most powerfully in reverse: when the requirement is missing, the result it guards is ruled out.
'Only if' states a requirement rather than a guarantee, so satisfying it removes an obstacle without settling whether permission is given.
'If and only if' makes the condition both necessary and sufficient, which is the one case where a rule may safely be read in either direction.
'Unless' means 'if not': without renewal the closure would be certain, so a stall still trading shows the renewal happened.
Necessary conditions filter applicants without selecting them, so something further is still required before the outcome is settled.
A sufficient condition is enough on its own, so meeting it settles the result, though it leaves open whether other routes to entry also exist.
A failed necessary condition blocks the result outright, whatever else was achieved. It also follows that he cannot have passed the practical, since that would have delivered the certificate.
'Only to' identifies a requirement, so anyone who has the result must have met it. The reverse claim, that every signatory gets access, is not stated.
A factor that is neither required nor enough carries no deductive weight, so its presence leaves the outcome entirely open.
Swapping the two halves and negating both gives the contrapositive, which always says the same thing as the original rule.
The converse simply swaps the two halves without negating them, and unlike the contrapositive it is not guaranteed to hold when the original does.
Assuming rain caused the closure is the 'affirming the consequent' error. The market could be closed for another reason.
Negating both halves produces the inverse of the rule, which does not follow from it. The original is silent about anyone outside the programme.
'Only' introduces a requirement rather than a guarantee, so it translates into a rule running from the result back to the condition.
The rule only says certified divers wear wetsuits. It doesn't say only certified divers do, so Tomas's status is undetermined.
Rewriting the ban as a conditional gives 'if unregistered, then barred', so a vehicle that is not barred cannot be unregistered.
Denying the result of a conditional lets you deny its condition, and that valid pattern is known as modus tollens.
The rule guarantees passability when the tide is out but does not reserve passability for that case, so the result cannot be read backwards.
The contrapositive turns 'not returned' into 'not incomplete', and the item states the rule was applied correctly, so no breach is involved.
An 'and' statement asserts each part separately, so denying either part contradicts it outright. Details the statement never mentions are merely unknown, not false.
This is a valid disjunctive syllogism: if at least one of two options is true, and one is false, the other must be true.
Denying a combined claim means at least one part fails; once the first part is known to hold, the failure must lie with the second.
'Neither … nor' denies both items at once, so each one may be denied separately. It gives no explanation for the failures.
'But never both' makes the choice exclusive, so confirming one option rules the other out, something a plain 'or' would not license.
An inclusive 'or' is satisfied as soon as one option holds, so confirming that option leaves the other entirely open.
Denying an 'or' denies both options at once, because a single true option would have made the original claim true.
Either trigger on its own would have set a working alarm off, so silence rules both triggers out together.
With exactly one option true and two of them eliminated, the remaining option must be the true one.
Both parts together guarantee the award, so a missing award with one part satisfied points to the other part failing.
'Ahead of' passes along a chain, so anyone ahead of Ben is also ahead of whoever Ben beats.
Fixing the top and bottom books leaves two middle slots, and the 'directly above' pair can fill them in only one order.
Rita is third, so two people stand ahead of her; Sam is therefore fourth, with Rita and those two ahead of him.
One town has a neighbour on each side along the same line, which is exactly what it means to be in the middle.
Two named candidates sit above fourth place, and one of that pair sits above the other, which forces the higher of them into the top two.
Chaining the two 'immediately behind' clues from the fixed position fills the next two slots in order, landing one of them in fifth place.
Linking each comparison end to end produces one complete order from highest to lowest, and third place falls straight out of it.
Ruling out the two ends leaves three possible slots, and nothing in the item narrows those three to one.
The survey has to come before the report's fixed day, so any later day is impossible while earlier days all remain open.
The middle of seven floors is the fourth, since three lie below it and three above; counting two floors up from there gives the answer.
One role is taken outright and another is barred, which leaves a single role available for the person under the restriction.
Removing both string options and the flute from Ben's list leaves one instrument, so his choice is settled without needing the other pupils.
The heaviest parcel is excluded from one city outright, and it cannot be the lightest, which quietly rules out a second city as well.
The opposite pair is fixed first, which reserves two sides; naming the left-hand neighbour then leaves only the right-hand side for the last person.
Start with the box carrying two exclusions, since it can hold only one colour; the remaining exclusion then decides the other two boxes.
Test each position for the linked pair on the three free floors, then discard the arrangement that forces a department onto the floor it is barred from.
One order is given outright, and the exclusion removes the coffee from one of the two people left, leaving only one candidate.
First narrow the earlier person to the days left open, then shift that whole set one day later for the person who follows.
Someone who must have a neighbour above them cannot be on the top floor, and the stated exclusion removes a second candidate, leaving one.
Two fixed positions leave a pair of adjacent slots, and the left-to-right clue puts that pair in only one possible order.
The argument reads silence as success, which holds only if complaints reliably track the underlying problem.
A recommendation supported by an outcome quietly treats that outcome as desirable; without that step the stated reason lends no support at all.
The argument moves from an achievement to an ability, a step that works only if the achievement really demands that ability.
Generalising from one setting to another requires the two settings to be alike in whichever respect the argument depends on.
Supplying the general rule that links the evidence to the conclusion is what turns a bare fact into an argument.
A rival explanation for the very same change undercuts the claim that the intervention produced it.
A high success rate can reflect who chose to take part rather than how hard the test was, which is a selection effect.
Without a comparison group, a recovery rate cannot show that the treatment rather than time made the difference.
Asking only the people who stayed leaves out those who left, so the wider claim holds only if the missing group would not change the picture. This blind spot is called survivorship bias.
A missing finding is not a finding. Failing to establish a claim leaves the question open rather than settling it the other way.
A false dilemma squeezes a range of possibilities into two, hiding middle paths such as shorter hours or a relocated stage.
Long service may make someone worth listening to, but it does not by itself make any particular proposal correct.
Circular reasoning assumes what it sets out to show, leaving a listener with no independent reason to accept it.
Two cases cannot stand in for a town; a claim about a population needs evidence drawn more broadly from it.
Recasting a modest proposal as an extreme one attacks a straw man instead of the position actually held.
Popularity and quality are separate questions, so an argument crossing from one to the other needs a bridge it has not supplied.
Predicting a chain of consequences requires evidence that each link actually follows; without it the alarming end point is asserted rather than shown.
An appeal to tradition mistakes how long something has lasted for how well it works, and those are different questions.
Warm weather plausibly drives both figures upwards, so their rising together says nothing about one producing the other.
Reasoning from parts to whole, the fallacy of composition, fails whenever the property accumulates, and enough light parts make a heavy machine.
Chain the two conditionals into a single rule running from customs to restocking, then apply it backwards: a false end result makes the first condition false.
The two rules chain into one: every member has trained recently, so failing that test rules membership out.
Chained rules run in one direction only, so a true end result does not travel back up the chain unless each step is stated as the sole route.
Work forwards from the stated use: the user must appear in the log, only one name is there, and the training rule then applies to that person.
Read the chain backwards twice: no signs means the sprinklers are running, and running sprinklers mean the reservoir is not low.
The inspection time changes nothing; the two conditionals chain together and are then run backwards from the refund that never happened.
Reference books are all catalogued and catalogued books never leave, so anything that left cannot have come from that section.
Follow the chain backwards from the missing acknowledgement: no acknowledgement means no pair of references, and without those the registration rule cannot have been satisfied.
The unlit security light rules out the north gate through the conditional, and the either-or statement then forces the remaining option to hold.
Two conditionals run backwards from the missing notification to rule out an early delivery, and the exclusive either-or then leaves a single option. The closing time plays no part in the deduction.