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NSW SelectiveYear 7 entry

If-then reasoning in Selective Thinking Skills

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If-then reasoning means following a rule that only runs one way. In Selective Thinking Skills, a rule like 'if it rains, the ground gets wet' means wet ground doesn't prove rain, but dry ground proves it didn't rain.

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The full lesson is in the SelectiveReady app. A free account opens How and Why Authors Write; this lesson needs a paid plan.

Updated 16 October 2026 · Facts checked 12 October 2026

If-Then Reasoning (lesson preview)

A short preview from the SelectiveReady lesson “If-Then Reasoning”, on if-then reasoning for the NSW Selective test.

Published:

Read the video transcript

This weapon is called the contrapositive. I know it sounds a little fancy, but the idea is actually really simple. You take your original one-way street, you flip it backwards, and you make both parts the opposite. You negate them, and the magic here is that this new statement you just built is 100% as true and reliable as the original one was. Let's see it in action with our rain example. The original was if it rains, the ground gets wet. So to get the contrapositive, first we flip it, so we start with the ground. Then we negate both parts, so the ground gets wet, becomes the ground is not wet, you know, it's dry, and it rains, becomes it did not rain. So our new totally true statement is, if the ground is dry, then it definitely did not rain. See that? It's the safe way to go backwards.

If-Then Reasoning is a full lesson in the SelectiveReady app. A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published. The preview has English and Chinese captions.

2

What will your child learn in this lesson?

Your child learns to treat every if-then rule as a one-way street. They'll be able to say what follows from a rule, reason backwards safely with the contrapositive, link rules into a chain and refuse the illegal U-turn.

The clip builds the contrapositive from one rule: if it rains, the ground gets wet. The full lesson adds the one-way street rule, chains, the three traps and two quiz questions.

3

How do if-then questions show up in Selective Thinking Skills?

Your child meets a rule in words, often about school life, and decides which conclusion follows. The Department says the section needs no previous knowledge. 2NSW Education · 12 October 2026 · Published

The Thinking Skills testWhat it means for if-then rules
402NSW Education · 12 October 2026 · Published questions in 402NSW Education · 12 October 2026 · Published minutesRewrite the rule as if and then before reading the options
42NSW Education · 12 October 2026 · Published options per questionCheck every option for a rule run backwards
a range of question types, shown in the practice tests2NSW Education · 12 October 2026 · PublishedIf-then rules can also hide inside puzzles and arguments
The practice papers say there are no marks lost for incorrect answers3NSW Education · 13 October 2026 · PublishedIf unsure, choose the safest move and go on
4

What is if-then reasoning?

An if-then rule says one thing always leads to another. The if part is where you start; the then part is where you must end up. The rule never says the trip works in reverse.

Each rule allows four moves, and only two are safe. Here they are with the lesson's rain rule.

You knowCan you be sure?With the rain rule
The if part happenedYes: the then part followsIt rained, so the ground is wet.
The then part happenedNo: something else may have caused itThe ground is wet. A sprinkler could have done it.
The if part didn't happenNo: the then part may still happenIt didn't rain. A hose could still wet the ground.
The then part didn't happenYes: the if part can't have happenedThe ground is dry, so it didn't rain.

The last row is the contrapositive. It's the safe way to reason backwards.

5

What is the method for if-then questions?

Rewrite the rule, find which part you've been given, then make a safe move. Everything else is a trap.

The one-way rule: if it rains, the ground gets wet. No U-turn: wet ground doesn't prove rain. Safe way back: dry ground means no rain.

  1. Rewrite the rule as if and then

    Every student who finishes gets a ribbon becomes: if a student finishes, then they get a ribbon.

  2. Find what you're told

    Is the new fact the if part, the then part, or one of them not happening?

  3. Make a safe move

    Forward from if to then. Or flip and negate: not then means not if.

  4. Stop at the U-turn

    Then does not prove if, and not if does not prove not then. Nothing certain follows.

How do chains of rules work?

When the then part of one rule is the if part of another, the rules link like dominoes. If it rains, the ground gets wet; if the ground is wet, the grass grows. So if it rains, the grass grows.

Chains only run forward. Growing grass doesn't prove it rained.

6

What does a worked if-then question look like?

We wrote this question to show the method.

Our practice rule
In the school library, every new book is kept on the front shelf. The book about volcanoes is not on the front shelf.

Question: Which one of these must be true?

OptionStatement
AThe volcano book is not a new book.
BEvery book on the front shelf is new.
CMr Lee forgot to put the volcano book on the front shelf.
DThe volcano book is on the back shelf.
StepWhat your child does
RewriteIf a book is new, then it's on the front shelf.
What's givenNot on the front shelf: the then part didn't happen.
Safe moveFlip and negate: the book is not new. Answer A.
Check the restB runs the rule backwards. C breaks the rule, which the question says is true. D might be true, but nothing forces it.
7

What mistake do children make with if-then rules?

The classic mistake is the illegal U-turn: treating the then part as proof of the if part. It sounds natural, which is why the lesson calls it the first trap.

TrapExampleThe fix
The U-turnThe ground is wet, so it rained.Ask: could anything else cause the then part?
Not if, so not thenIt didn't rain, so the ground is dry.The rule says nothing about days without rain
Backwards through a chainThe grass grew, so it rained.Dominoes fall forward only
8

Can my child try one on their own?

Here is a question from our free Thinking Skills set. Two children each reason from the same rule, and your child decides who is right.

Practice question · SEL-TS-TST-04

At the school cross-country carnival, every student who finishes the course is given a ribbon.

Ji-woo says: "Tama has a ribbon, so he must have finished the course."

Hannah says: "Lucy was not given a ribbon, so she did not finish the course."

If the information in bold is true, whose reasoning is correct?

  1. A

    Ji-woo only

  2. B

    Hannah only

  3. C

    Both Ji-woo and Hannah

  4. D

    Neither Ji-woo nor Hannah

Show answer and explanation

Answer: B

Answer: B (Hannah only)

  1. The rule says that finishing the course is enough to get a ribbon. It does not say finishing is the only way to get one.
  2. Ji-woo: Tama might have been given his ribbon for some other reason, so we cannot be sure he finished. Ji-woo's reasoning is not correct.
  3. Hannah: if Lucy had finished, she would have been given a ribbon. She was not, so she cannot have finished. Hannah's reasoning is correct.

Why the other options are wrong

  • A (Ji-woo only): Ji-woo turns the rule around: it says finishers get ribbons, not that only finishers get them.
  • C (Both Ji-woo and Hannah): Hannah is right, but Ji-woo's reasoning turns the rule around, so it is not both.
  • D (Neither Ji-woo nor Hannah): Hannah's reasoning does follow, because anyone who finished would have a ribbon and Lucy has none.

  1. Rewrite

    If a student finishes the course, then they get a ribbon.

  2. Ji-woo

    Tama has a ribbon, so he finished. That's the U-turn: a ribbon could come another way.

  3. Hannah

    Lucy has no ribbon, so she didn't finish. That's flip and negate, a safe move.

  4. Answer

    B, Hannah only.

9

How can my child practise logical reasoning at home?

Short talks about everyday rules work well, because the rules are everywhere. Five minutes in the car counts.

Spot the rule

Find if-then rules in signs, games and school notes. Rewrite each one with if and then.

Flip and negate

Take a rule and say its contrapositive. Then say the U-turn and explain why it fails.

Does it follow?

One person states a rule and a fact. The other says follows, doesn't follow or can't tell.

Try the real screen

The Department's online practice tests copy the real test. 2NSW Education · 12 October 2026 · Published

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Questions parents ask about if-then reasoning

What is a contrapositive?

It's a rule flipped and negated. If it rains, the ground gets wet becomes: if the ground is dry, it didn't rain. Both are equally true.

What is the converse?

The rule turned around: if the ground is wet, it rained. It isn't safe, and it's the classic trap.

Is if-then reasoning the same as deduction?

It's one kind of deduction. The deduction lesson adds all and some statements.

Is the full lesson free?

A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published.

Next questions

Selective Thinking Skills →Lesson: Thinking Like a Detective →Lesson: Judging Arguments →Lesson: Solving Logic Puzzles →Free Selective practice test →

Sources and checks

  1. SelectiveReady

    SelectiveReady · Checked 13 October 2026

  2. Selective high school practice tests

    NSW Department of Education · Checked 12 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Page text: CC BY 4.0.

  3. Selective High School Placement Test, Thinking Skills Question Paper, Practice Test 1 (2026 entry practice tests, PDF)

    NSW Department of Education · Checked 13 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Quoted briefly with credit. Saved text: the cover-page instructions only; the question pages are not stored (W§3.22).

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