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Reasoning Foundations

Must-Be-True Conclusions

Must-Be-True Conclusions teaches a transferable deductive conclusions routine for selective and scholarship reasoning questions. Students learn the exact first move, the proof step, and the main trap to avoid before timed practice.

  • Separate what must be true from what could be true.
  • Chain two or more facts without reversing a rule.
  • Reject options that copy words but are not guaranteed.
Free sample lesson — reading only

Lesson overview

What this free sample teaches

Use the deductive conclusions routine to choose an answer and name the trap avoided.

Focus

  • Question family: deductive conclusions.
  • Core move: Start from a named fact, apply each rule in order, then test whether the answer could be false while every fact stays true.
  • Main trap: Choosing an option that sounds related but is only possible.

What gets tested

  • NSW/VIC/scholarship fit: NSW thinking skills and scholarship deductive reasoning.
  • Choosing the answer that is justified by the stated information.
  • Explaining why the strongest distractor fails.

Quick guide

  • Read the final question before the options.
  • Name the reasoning family and first move.
  • Use the stated facts or relationship, not outside knowledge.

Success criteria

  • Separate what must be true from what could be true.
  • Chain two or more facts without reversing a rule.
  • Reject options that copy words but are not guaranteed.

teach

Teach: Must-Be-True Conclusions

A must-be-true answer is locked in by the stated facts.

Must-Be-True Conclusions is a core reasoning lesson for NSW thinking skills and scholarship deductive reasoning. The aim is to prove the answer from the question, not to guess from topic familiarity.

A must-be-true answer is locked in by the stated facts. Students should treat this as a proof task: the answer must be supported by the facts, rules, data, relationship or argument in the question.

The routine is: Start from a named fact, apply each rule in order, then test whether the answer could be false while every fact stays true. This routine works across NSW, VIC and scholarship contexts because it focuses on the reasoning structure rather than the test label.

The common trap is Choosing an option that sounds related but is only possible. Strong students are often caught because the wrong answer is partly relevant. The fix is to name exactly why that option is not justified.

Reasoning family

deductive conclusionsIt tells you the first move.

Proof move

Start from a named fact, apply each rule in order, then test whether the answer could be false while every fact stays true.It links the answer to the question.

Distractor trap

Choosing an option that sounds related but is only possible.It explains why a tempting option fails.
Anatomy of deductive conclusions
  1. Question cluedeductive conclusions
  2. Core evidencefacts, rules, data, words or argument links supplied in the item
  3. Reasoning moveStart from a named fact, apply each rule in order, then test whether the answer could be false while every fact stays true.
  4. Trap checkChoosing an option that sounds related but is only possible.
  5. Answer shapeThe facts force ..., because ... then ...

The moveClassify the task, apply the routine, prove the answer, then reject the closest trap.

  • Separate what must be true from what could be true.
  • Chain two or more facts without reversing a rule.
  • Reject options that copy words but are not guaranteed.

show

Show: must-be-true conclusions worked end to end

Watch the decisions, not just the answer: what the question is really asking, how the proof is built, which option is designed to catch you, and what a deeper reading of the same answer adds.

The item is on the card above, with its options. Work down the six steps in order. Steps 1 to 3 are the thinking that happens before an option is marked; steps 4 to 6 are the same answer at two depths, and what the deeper one buys you.

Full item: three facts, one question, four options

Question: Three facts are given about the debating squad, the speech workshop and the practice booklet. Which conclusion must be true — not merely possible?

The debating squad

  • Every student in the debating squad attends the speech workshop.
  • Every student who attends the speech workshop receives a practice booklet.
  • Tara is in the debating squad.

Which conclusion must be true?

A. Tara has read the practice booklet. B. Tara receives a practice booklet. C. Tara receives a practice booklet at the speech workshop. D. Every student who receives a practice booklet is in the debating squad.

  1. Step 1 — Read the question for the word 'must'

    Four options. Three of them are things that could happen; only one is forced.

    The question does not ask which conclusion is likely, or which one a sensible person would expect. It asks which one must be true, and that single word decides how I read all four options.

    Must be true means this: if I accept the three facts exactly as written, is there any way this option could still be false? If there is a way — even an odd one — the option is out. It does not have to be unlikely. It only has to be possible.

    So my proof has to be a chain, not an impression. Two of the three facts are rules with the word 'every' in them, and rules with 'every' can be joined end to end. The third fact is not a rule at all: 'Tara is in the debating squad' names one person and stands her at one end of that chain.

    That is the shape of the work. Start at Tara, walk along the rules in the direction they were written, and stop the moment the rules stop talking. Whatever I have reached at that point is the answer. Whatever is one step past it is a trap.

    • It asks which one must be trueSwap 'must be true' for 'could be true' and three of these four options become defensible. The whole difficulty of the item lives in one word, and it is not a word about debating or booklets — it is a word about how much proof is being demanded. Read it before you read the facts.
    • It does not have to be unlikely. It only has to be possible.The test for throwing an option out is deliberately generous: one way it could still be false is enough, however strange that way is. Marks are lost here by dismissing the odd possibility as unrealistic, when unrealistic is exactly what this kind of question allows you to use.
    • rules with 'every' can be joined end to endTwo of the three facts start with 'Every'; the third names a person. That is not decoration. A rule with 'every' in it is a link that will join to another link, and 'Tara is in the debating squad' is the hook you hang the chain on. Sort the given information into rules and people before you look at a single option.

  2. Step 2 — Walk the chain from Tara, and stop where the rules stop

    Two joins and a deliberate halt. The halt is what the answer is made of.

    Take the facts in the order that lets them connect.

    • Start: Tara is in the debating squad. This is the only fact about a named person, so it is the only place a chain can begin.
    • Join 1: every student in the debating squad attends the speech workshop. Tara is in the squad, so Tara attends the workshop. Nothing here is a guess — 'every' leaves no squad member out, and Tara is a squad member.
    • Join 2: every student who attends the speech workshop receives a practice booklet. Tara attends the workshop, so Tara receives a practice booklet.
    • Halt: there is no third rule. The facts say what happens to squad members and what happens to workshop attenders, and then they stop talking.

    What that rules in: Tara receives a practice booklet, reached by two joins, each one running forwards along a rule that says 'every'.

    What it rules out: anything about what Tara does with the booklet afterwards, anything about where it was handed to her, and anything about students who are not in the squad.

    Answer: B.

    • Tara is in the squad, so Tara attends the workshop.The first join, and it is worth being slow about why it is safe. The rule covers every student in the debating squad, and Tara is one of them, so the rule reaches her personally. A rule you cannot place a named person inside is a rule you cannot use yet.
    • Halt: there is no third rule.The most valuable line in the working is the one that reports that nothing happened. Two rules give two joins and then the facts stop talking. Saying out loud where the given information runs out is what separates the answer from the option sitting just past it.
    • anything about where it was handed to herWritten down before the options are read, on purpose. Every student who attends the speech workshop receives a practice booklet — attending is the condition for getting one, and a condition is not a place. Listing what the facts refuse to settle builds your trap list in advance.

  3. Step 3 — The option that is the answer plus four extra words: C

    C contains B and then says where it happened. Those four words came from nowhere.

    The option most students choose after B: C — 'Tara receives a practice booklet at the speech workshop.'

    Why they choose it: it is not a rival to B. It contains B. Every word of the correct answer sits inside it, and the extra words describe the very workshop the chain ran through. Squad, then workshop, then booklet — the workshop is genuinely part of the reasoning, and it feels tidy to say where a thing that arrived actually arrived.

    Which step it skips: it never asks what the second rule is a rule about. 'Every student who attends the speech workshop receives a practice booklet' makes attendance the condition for receiving one. It does not say the booklet is handed over during the workshop. Attend in March, and the school could post the booklet in April; all three facts would still be true and C would be false. That is enough — a must-be-true option only has to fail once.

    Corrected reasoning: an option that contains the answer is not therefore safe. It is safe only if every one of its words is forced. Read the extra words on their own and hunt for the fact that produced them. Here nothing produced 'at the speech workshop' except the sound of the chain.

    • It contains B.This is why C is the hard one and D is not. D runs a rule backwards and reads wrong almost immediately; C agrees with everything the chain proved and then walks one step further. In a must-be-true question the dangerous option is rarely the opposite of the answer — it is the answer with something added.
    • Attend in March, and the school could post the booklet in AprilAn invented month, doing real work. To knock out an option you need one world where every given fact holds and the option fails, and a school that chooses to post the booklet later is such a world. It does not matter that no school in the item posts anything; it matters that nothing in the item stops it.
    • Read the extra words on their own and hunt for the fact that produced them.The habit this trap is worth learning for. Cover the part you agree with, look only at 'at the speech workshop', and ask which sentence says it. There is no such sentence: attendance is the condition for receiving one, not the place of delivery. An option is only as forced as its weakest phrase.

  4. Step 4 — The answer, and why it is forced

    Two joins, each naming its rule, then one paragraph on why the nearest option fails. Three paragraphs in all.

    B must be true. Tara is in the debating squad, and every student in the debating squad attends the speech workshop, so Tara attends it. Every student who attends the speech workshop receives a practice booklet, so Tara receives a practice booklet. Both joins use a rule that says 'every', so there is no student the rule could have missed and no step that rests on what is likely.

    C is the closest wrong option. It repeats the correct conclusion and adds 'at the speech workshop'. The second rule makes attending the workshop the condition for receiving a booklet; it never says the booklet is handed over there. Because the facts do not settle where, C could be false while all three facts stay true, and an option that could be false is not an option that must be true.

    That is enough to be right: it names the rule each join uses, it reaches the conclusion in the direction the rules were written, and it says exactly which words of the nearest option have no fact behind them.

    • there is no student the rule could have missedWhy 'every' was quoted in both joins instead of paraphrased. Change the second rule to 'most students who attend the speech workshop receive a practice booklet' and Tara's case springs open again, because most is not all. Quote the quantifier as well as the rule: it decides whether you are holding a proof or a strong guess.
    • an option that could be false is not an option that must be trueThe sentence that finishes the rejection, and it is deliberately unexcited. The answer never calls C false — in most real schools C would be true. It says C could be false while all three facts stay true, which is the only charge this kind of question lets you bring.

  5. Step 5 — Going deeper: one-way arrows, and where each wrong option sits

    Same three facts, same chain, same option B — but the arrows now have a direction and every wrong option has an address.

    B must be true, and it is worth saying why the chain can be walked in one direction only. Both rules are one-way. 'Every student in the debating squad attends the speech workshop' puts squad members inside the workshop and says nothing whatever about an attender who is not in the squad. The chain therefore has an entrance and an exit, and Tara was placed at the entrance.

    The chain also has an end, and the end is the most informative thing in the item. It runs squad, then workshop, then booklet, and there the facts fall silent. Everything the item can prove lives inside those two joins; everything the three wrong options offer lives outside them, and it pays to be precise about where each one landed.

    D sits before the chain, running a rule backwards: 'every student who receives a practice booklet is in the debating squad' would need a rule the item never wrote. A sits after the chain: the booklet reaches Tara's hands, and reading it is a separate act nobody mentioned. C sits alongside the chain, agreeing with both joins and adding a fact about place that neither join carries.

    That is what makes C the expensive mistake. A and D can be dismissed by noticing a direction and noticing an extra event. C survives both of those checks, because it gets the direction right and adds no event at all — it adds a circumstance. The only way to catch it is to read its extra words apart from its correct words and ask, of 'at the speech workshop', which sentence in the item would have to exist for this to be forced.

    Step 4 proved B and saw off C, and that verdict stands untouched. What is different is that the two rules now carry a direction, so D stops being merely wrong and becomes predictable, and each rival has an address relative to the chain — before it, after it, beside it — which is what stops C arriving as a surprise. Proving the conclusion and beating the nearest rival is enough to be right today. Showing that all three rivals were manufactured out of the same two joins, and naming the part of the chain each one abused, is what makes the next chain item easy.

    • The chain therefore has an entrance and an exit, and Tara was placed at the entrance.Step 4 walked the chain; this says why walking it the other way is not on offer. 'Every student in the debating squad attends the speech workshop' says nothing whatever about an attender who is not in the squad, so the rule points one way and option D is the item checking whether you noticed.
    • before it, after it, beside itThe map Step 4 did not draw. D runs a rule backwards, A adds an event past the end, and C adds a circumstance alongside. Three wrong options, one chain, three different ways of leaving it — and once you can name the position, the option that agrees with both joins stops looking safe.
    • it adds a circumstanceThe distinction this whole step was built to reach. A adds an event — reading — which is easy to spot because something new happens. C adds a fact about place and nothing happens at all, so a reader checking for extra events sails straight past it. Circumstances are quieter than events and cost the same mark.

  6. Step 6 — What the deeper reading buys you next time

    Two answers, three facts, one option — and a difference that lives entirely in what each can say about the rivals.

    Enough to be rightEnough to be right next timeWhat it adds
    Joins the two rules and quotes 'every' at each join.Adds that both rules are one-way, so the chain has an entrance and an exit.It explains why option D exists instead of merely rejecting it.
    Rejects C because the facts do not settle where the booklet is handed over.Says C adds no event, only a circumstance, which is why the usual check for extra happenings misses it.It names the reason a good student falls for C, not just the reason C is wrong.
    Deals with the one wrong option that is nearest.Places every wrong option relative to the chain: before it, after it, beside it.It turns one solved item into a way of predicting the next one.

    The three facts and the option are common ground. What is not common is how much of the item's design each reading can see.

    • Places every wrong option relative to the chain: before it, after it, beside it.Both answers reject C; only one of them could have said in advance where a wrong option would come from. Predicting the shape of the distractors is the difference between getting this item right and getting the next one right, and the next one will use a different squad and the same two joins.
    • Rejects C because the facts do not settle where the booklet is handed over.Stopping at unsettled is enough to mark the right letter, and Step 4 stops there. The deeper reading goes on to say why unsettled was hard to see: C adds no event, only a circumstance, so nothing new appears to check.

compare

Compare: weak vs strong reasoning

See the difference between topic matching and proof.

The weak answer reacts to the surface topic. The strong answer proves the relationship or rule.

The whole response

Weak answer

Tara must be one of the best speakers.

Strong answer

Tara receives a practice booklet because squad member -> workshop -> booklet is a forced chain.

Point-by-point breakdown3
  • First moveWeaker: Looks for a familiar word or number.Stronger: Uses the deductive conclusions routine.The routine keeps the answer tied to evidence.
  • ProofWeaker: Gives a plausible answer without a clear link.Stronger: Shows how the stated information supports the answer.Reasoning questions reward justified conclusions.
  • Trap controlWeaker: Choosing an option that sounds related but is only possible.Stronger: Names why the distractor fails.Trap awareness improves transfer to mixed timed sections.

guide

Guide: checkpoint

Do one reasoning move before independent practice.

Answer in one sentence using the lesson's sentence starter.

All blue folders are locked. This folder is blue. What must be true?

Want feedback on your own answer? Get started to practise with instant marking.

  • Separate what must be true from what could be true.
  • Chain two or more facts without reversing a rule.
  • Reject options that copy words but are not guaranteed.