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Chapter 0 wrap-up

Getting Ready to Reason

Closing thought

A statement is a sentence that gets exactly one stamp, TRUE or FALSE, and the stamp depends only on what the words promise. That is the thread through all four sections. Questions and commands get no stamp. A statement nobody can check yet still has one; we just don't know which. And "some," "all," "only," and "or" promise less, or something different, than a quick reader hears.

So go back to the refund message. "Some customers got a full refund" is the only statement in it, and it promises one refund to someone, somewhere. To test a claim like "all customers got refunds," you now picture one specific customer who didn't. Next, Chapter 1 takes these statements and asks what it means to back one up with reasons.

Chapter review

One practice set per topic this chapter taught — same fixed, ungraded ladders as the practice panels inside each section.

Practice: Statements, questions, and commands (4 problems · doesn’t affect your progress)

Which sentence is a statement?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

This one asks about bagels without saying anything about them.

An instruction can be followed, not stamped.

This is a happy noise about bagels. It says nothing that could turn out true or false.

Why

Only “The bakery sells bagels” says something is the case, so only it has a truth value.

Which one could you answer with “That’s false”?

The bakery sells bagels.

“The first person to walk on Mars will be a woman.” Is it a statement?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

Unknown is not the same as stampless. Once someone walks on Mars, the stamp will be clear.

A prediction tells you something will happen. It doesn’t ask.

Why

It makes a prediction, so it has a truth value that nobody knows yet. It is a pending statement.

Will a stamp fit once someone walks on Mars?

Yes. It is a prediction; a stamp fits, though nobody knows which.

Sort each sentence from a gym’s sign-in screen.

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

What this task checks

Structure checked automatically. Whether your ideas are convincing isn't graded, so reread with the checklist.

The compiler says

A model answer

Why

The pool hours and the broken locker can each be checked. The scan instruction and the question can’t be stamped.

Correct answer

Also accepted:

Why

Two sentences report facts about the gym.

“The pool closes at 8 p.m. tonight.” → Statement; “Scan your card to enter.” → Not a statement; “Have you tried our new spin class?” → Not a statement; “Locker 14 is out of order.” → Statement

Which reason for calling a sentence “not a statement” is a good one?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

Unknown truth doesn’t remove the stamp. Many statements are still pending.

False statements are still statements. FALSE is one of the two stamps.

Private facts are still facts. Only the person who has the thought can check, but a stamp still fits.

Why

A sentence fails to be a statement when it doesn’t say anything is the case, like a question or command. Being unknown, false, or private doesn’t stop a sentence from being a statement.

Which reason is about the sentence’s job, not about what anyone knows?

It asks instead of saying anything is the case.

Practice: What a sentence commits you to (4 problems · doesn’t affect your progress)

Every plant in the garden bloomed. Is “Some plants in the garden bloomed” true?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

“Not all” is only a hint. The sentence never says it.

“Every” would say more, but “some” still holds.

Why

At least one plant bloomed, so “some plants bloomed” is true.

Replace “some” with “at least one.”

Yes. At least one bloomed.

“All winners will be notified by email.” The contest had no winners. Is the sentence false?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

“All” never promises that winners exist. It only says what happens to each one there is.

Every statement has exactly one stamp. With nothing to break it, it is TRUE.

Why

With no winners, there is no un-notified winner, so nothing breaks the sentence. It is true.

What would break the sentence?

No. Only an un-notified winner could make it false.

“You can register online or by phone.” Omar starts online and finishes by phone. Did he follow the instructions?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

That is the exclusive reading, which needs words like “not both.” None appear here.

The sentence allows either way, and using both still fits.

Why

The “or” is read inclusively, so using both methods follows the instructions.

Look for words that rule out both.

Yes. With no “not both,” using both is allowed.

“Only residents may use the gym.” Which case does NOT go against it?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

A visitor using the gym is exactly what the sign rules out.

The delivery worker isn’t a resident, so using the gym goes against the sign.

Why

The sign says everyone who uses the gym is a resident. A resident being turned away doesn’t break that.

“Only” limits who may use the gym. It doesn’t promise every resident gets in.

A resident is turned away during a class.

Practice: True, false, and possible (4 problems · doesn’t affect your progress)

The train left on time. “The train left late” is…

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

A late train contradicts nothing; it just didn’t happen this time.

The train left on time, so this sentence is false.

Why

In fact the train was on time, so the sentence is false. A late departure is still possible.

Answer “is it true?” and “could it be true?” separately.

false but possible.

Which is impossible?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

Locked all night contradicts nothing.

A never-locked door is possible, if unwise.

Why

A door can’t be locked and unlocked at the same moment, so that sentence is impossible.

Which sentence takes back what it says?

The door is locked and unlocked at the same moment.

Which scenario shows that “Every book in the library is in English” could be false?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

An English novel fits the claim.

The bookstore isn’t part of the claim.

Why

One Spanish cookbook in the library makes the claim false.

You need one book in the library that isn’t in English.

The library holds a Spanish cookbook.

Does “Every chef in the kitchen wore an apron” guarantee “Everyone wearing an apron in the kitchen was a chef”?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

They seem alike, but a scenario pulls them apart: add a dishwasher in an apron.

A chef without an apron makes the first sentence false, so it doesn’t test the guarantee.

Why

Every chef wears an apron, and so does the dishwasher. The first sentence holds and the second fails, so the first doesn’t guarantee the second.

Build a kitchen where the first sentence is true and the second is false.

No. A dishwasher in an apron makes the first true, the second false.

Practice: How to practice (4 problems · doesn’t affect your progress)

Which rung asks you to tell an idea apart from something that only resembles it?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

Recognizing picks out an example when the idea is named for you.

Applying uses the idea on a new case.

Building makes your own example.

Why

The top rung, spot the look-alike, compares the idea with a near miss.

It is the top rung.

Spot the look-alike

What do most mistakes in this chapter’s material come from?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

Most items here don’t need special knowledge. They need careful reading.

Hints used well help. They aren’t the usual source of errors.

Why

Small words like some, all, only, or, and not change what a sentence promises. Slow reading catches them.

Think of “some,” “only,” and “or.”

Reading too fast and missing a small word

Put the four rungs of a practice ladder in order, from first to last.

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

What this task checks

Structure checked automatically. Whether your ideas are convincing isn't graded, so reread with the checklist.

The compiler says

A model answer

Why

Recognize, apply, build, then spot the look-alike. Each step leans on the ones before it.

Correct answer

Also accepted:

Why

Each rung needs the one below it.

Recognize → Apply → Build → Spot the look-alike

Mateo can pick out “or” sentences easily but keeps misjudging whether they are true. Which rung needs work?

Correct! 🎉 Not quite.

Right on try — credit. Right — the answer had already been shown, so no credit this time. Next try is worth Answer shown after three tries — this one no longer earns credit. You chose to see the answer — this one earns no credit.

He already recognizes “or” sentences. That rung is fine.

Building comes after applying, so it can’t be where the trouble starts.

The look-alike rung sits above apply. Fix apply first.

Why

Judging a given case is applying. Mateo should work apply items, likely checking how “or” handles both parts being true.

Judging whether a given sentence is true is which rung?

Apply

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