Read the lesson text

teach

Teach: what must be true?

The answer is the one the facts prove. Nothing more.

A must-be-true question asks for the one answer the facts prove. You don't pick what's likely or what sounds sensible. You follow the facts, and you stop where they stop.

A must-be-true answer is locked in by the facts. If every fact stays true, the answer can't be false. 'Likely' isn't enough. 'Could happen' isn't enough either.

Here's the method. Start from the fact about a named person. Then follow each rule in the order it's written. Then test each option: can you think of a case where every fact is true but the option is false? If you can, it isn't a must.

The trap is an option that sounds related but is only possible. It often uses words from the question, so it feels right. Say which words in it have no fact behind them.

Every student in the debating squad goes to the speech workshop. Everyone at the workshop gets a practice booklet. Tara is in the squad. So Tara goes to the workshop, and so she gets a booklet. That must be true.

Now test 'Tara gets her booklet at the workshop'. Could it be false while the facts stay true? Yes. The school could post it to her later. The facts never say where she gets it, so this option isn't a must.

Conclusion

the answer the facts prove.In this lesson, it's the option that must be true.

Chain

joining rules in order: squad, so workshop, so booklet.Each link must follow the rule the way it's written.

A case that breaks it

a situation where every fact is true but the option is false.One such case shows the option isn't a must.

How to solve a must-be-true question

What's askedEvery squad student goes to the workshop. Everyone at the workshop gets a booklet. Tara is in the squad. What must be true?
The factsStart with the fact about Tara. Use only the two rules. Don't add anything.
Work it outTara is in the squad, so she goes to the workshop. So she gets a booklet. The rules stop there.
The trap'Tara gets it at the workshop' adds a place. The facts never say where.
The answerTara gets a practice booklet. Both rules say 'every', so no one is left out.

The moveRead the question. Follow the chain. Stop where the facts stop. Then test the tempting option.

You can tell apart what must be true and what could be true.
You can join facts in a chain, the way the rules are written.
You can reject an option that adds something the facts don't say.

show

Show: a worked example

Watch how to solve it, one step at a time.

Read the problem, then follow the steps. You'll see the answer, the trap, and what to do next time.

Full problem: three facts, four options

Question: Three facts are given. Which option must be true, not just possible?

The debating squad

Every student in the debating squad goes to the speech workshop.
Everyone who goes to the speech workshop gets a practice booklet.
Tara is in the debating squad.

Which of these must be true?

A.Tara has read the practice booklet.

B.Tara gets a practice booklet.

C.Tara gets a practice booklet at the speech workshop.

D.Everyone who gets a practice booklet is in the debating squad.

Step 1 — Read the question
Work out what kind of answer you need.
The question asks what must be true. It doesn't ask what's likely. So for each option, I'll ask: could this be false while all three facts stay true? If yes, it's out.

Two facts are rules that start with 'every'. One fact is about Tara. I'll start with Tara and follow the rules forward.
- It doesn't ask what's likely.Change 'must' to 'could' and three of the options would work. One word sets how much proof you need.
- could this be false while all three facts stay true?This is the test for every option. One case where it's false is enough to rule it out.
- Two facts are rules that start with 'every'.Sort the facts first: rules, and facts about a person. The person is where the chain starts.
Step 2 — Work it out
Follow the steps from the facts to the answer.
Follow the chain from Tara.
- Start: Tara is in the debating squad.
- Link 1: every squad student goes to the workshop. So Tara goes to the workshop.
- Link 2: everyone at the workshop gets a booklet. So Tara gets a booklet.
- Stop: there are no more rules.
The facts don't say what Tara does with the booklet. They don't say where she gets it. They don't say anything about people outside the squad.

Answer: B.
- So Tara goes to the workshop.'Every' means no squad student is left out. Tara is in the squad, so the rule includes her.
- Stop: there are no more rules.Saying where the facts stop is what separates the answer from the trap just past it.
- They don't say where she gets it.Write down what the facts don't tell you. That list shows you the traps before you read the options.
Step 3 — Spot the trap
See why a tempting answer is wrong.
Common wrong answer: C, 'Tara gets a practice booklet at the speech workshop.'

Why it tempts you: it contains the right answer, B. And the workshop really is part of the chain.

Why it's wrong: the rule says people at the workshop get a booklet. It doesn't say they get it there. The school could post it later. All three facts would still be true, but C would be false.

Fix: when an option has extra words, cover the part you agree with. Then ask which fact gives you the extra words.
- it contains the right answer, BThe dangerous option is often the right answer with something added.
- The school could post it later.A made-up case is fine. It only needs to keep every fact true.
- Then ask which fact gives you the extra words.No fact says 'at the workshop'. An option is only as certain as its weakest words.
Step 4 — The answer
Say the answer and the shortest proof.
B. Tara is in the squad, so she goes to the workshop. Everyone at the workshop gets a booklet, so Tara gets one. Both rules say 'every', so Tara can't be left out.

C adds 'at the workshop', and no fact says that. So C could be false while every fact stays true.
- Both rules say 'every', so Tara can't be left out.If a rule said 'most', Tara might be the one left out. Then nothing would be certain.
- So C could be false while every fact stays true.You don't have to show C is false. You only have to show it could be.
Step 5 — The method
What to remember for questions like this.
Rules only go one way. 'Every squad student goes to the workshop' tells you about squad students. It tells you nothing about other people at the workshop.

So each wrong option leaves the chain in a different way:
- D turns a rule around. It goes from booklet back to squad.
- A goes past the end. Reading the booklet is a new event.
- C adds a detail. It says where, and no fact does.
C is the hardest, because it adds no new event. Check every extra word, not just extra actions.
- Rules only go one way.This is why D is wrong. People outside the squad could get booklets too.
- So each wrong option leaves the chain in a different way:Turned around, past the end, or an added detail. Naming the trap helps you spot it next time.
- Check every extra word, not just extra actions.A place or a time is easy to miss, because nothing new happens.

Step 6 — Next time

What to do on your next question.

In this question	Next time	Why it helps
Started from Tara and followed both rules forward.	Start from the fact about a named person.	The chain can only start there.
Stopped where the rules stopped.	Say out loud where the facts run out.	Anything past that point is a trap.
Rejected C, which added 'at the workshop'.	Cover the words you agree with. Check the rest against the facts.	It catches an added place or time.
Rejected D, which turned a rule around.	Check which way each rule goes.	Rules only go one way.

Say out loud where the facts run out.This one habit catches A and C.
Check which way each rule goes.This catches D, and it comes up again in the next lesson.

compare

Compare: a guess, or a proof?

Picking what sounds right, or following the facts.

The weak answer picks what sounds sensible. The strong answer follows the facts and stops where they stop.

The whole response

Sounds right

Ravi must be good at science.

Follows the facts

Ravi is in the club, so he goes on the tour, so he gets a safety card.

Point-by-point breakdown3

First moveWeaker: Looks for something that sounds sensible.Stronger: Starts from the fact about Ravi.The chain can only start from a named person.
ProofWeaker: Gives an answer with no link to the facts.Stronger: Shows each link in the chain.Every part of the answer needs a fact behind it.
The trapWeaker: Picks an option that's only possible.Stronger: Says which words have no fact behind them.One case that breaks it rules the option out.

guide

Guide: try one together

One small step with help before you go solo.

Look back at the worked problem. Now try one like it.

Every member of a chess team goes to a strategy meeting. Everyone at that meeting gets a puzzle sheet. Visitors who don't go to the meeting can also get puzzle sheets. Priya has a puzzle sheet. Can we say Priya is on the chess team? Pick the answer the facts support. Then give the rule and a case that shows why having a sheet isn't enough.

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Keep each rule the way it's written.
Tell apart what's certain and what's only possible.
Give a case where every fact is true.

Your turn

Every robotics captain goes to the safety talk. Everyone at the talk gets a badge. Nila is a robotics captain. What must be true?

A. Only captains get badges
B. Nila gets it at the talk
C. Nila wears the badge daily
D. Nila gets a badge

All green permits can be used. Some permits that can be used are digital. This permit is green. Which is certain?

A. It is the only permit that can be used
B. It is digital
C. It can be used
D. All digital permits are green

Must-Be-True Conclusions