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Reasoning Foundations

If-Then and Only-If Rules

If-Then and Only-If Rules teaches a transferable conditional reasoning 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.

  • Translate if, only if, all, none and unless into usable rules.
  • Use the contrapositive when it is valid.
  • Avoid the converse and inverse traps.
Free sample lesson — reading only

Lesson overview

What this free sample teaches

Use the conditional reasoning routine to choose an answer and name the trap avoided.

Focus

  • Question family: conditional reasoning.
  • Core move: Write the rule as IF condition THEN result, mark whether it can be reversed, and check each option against the valid directions only.
  • Main trap: Treating 'if P then Q' as though it also says 'if Q then P'.

What gets tested

  • NSW/VIC/scholarship fit: NSW thinking skills, VIC verbal logic and scholarship deduction.
  • 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

  • Translate if, only if, all, none and unless into usable rules.
  • Use the contrapositive when it is valid.
  • Avoid the converse and inverse traps.

teach

Teach: If-Then and Only-If Rules

Conditional reasoning is about the direction of a rule.

If-Then and Only-If Rules is a core reasoning lesson for NSW thinking skills, VIC verbal logic and scholarship deduction. The aim is to prove the answer from the question, not to guess from topic familiarity.

Conditional reasoning is about the direction of a rule. 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: Write the rule as IF condition THEN result, mark whether it can be reversed, and check each option against the valid directions only. 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 Treating 'if P then Q' as though it also says 'if Q then P'. 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

conditional reasoningIt tells you the first move.

Proof move

Write the rule as IF condition THEN result, mark whether it can be reversed, and check each option against the valid directions only.It links the answer to the question.

Distractor trap

Treating 'if P then Q' as though it also says 'if Q then P'.It explains why a tempting option fails.
Anatomy of conditional reasoning
  1. Question clueconditional reasoning
  2. Core evidencefacts, rules, data, words or argument links supplied in the item
  3. Reasoning moveWrite the rule as IF condition THEN result, mark whether it can be reversed, and check each option against the valid directions only.
  4. Trap checkTreating 'if P then Q' as though it also says 'if Q then P'.
  5. Answer shapeThe valid direction is ... -> ..., so ...

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

  • Translate if, only if, all, none and unless into usable rules.
  • Use the contrapositive when it is valid.
  • Avoid the converse and inverse traps.

show

Show: worked reasoning

Follow the proof move, then compare the trap.

Read the problem, name the reasoning family, and watch how the answer is proved.

Full problem

Choose the answer that is best supported.

A school badge is awarded only if a student completes the service log. Leila has a school badge. Omar completed the service log. Which statement follows?

  1. Step 1 - Classify

    Name the job.

    This is a conditional reasoning question. The first move is: Write the rule as IF condition THEN result, mark whether it can be reversed, and check each option against the valid directions only.

    • Question familyNaming the family selects the right routine.

  2. Step 2 - Prove

    Use the stated information.

    Only-if means badge -> completed log. Leila has the badge, so her log completion is forced; Omar may or may not have the badge.

    • Proof moveThe answer is tied to the question, not to outside knowledge.

  3. Step 3 - Reject the trap

    Explain why the closest distractor fails.

    Tempting answer: Omar must have a school badge.

    Why it fails: Treating 'if P then Q' as though it also says 'if Q then P'.

    • TrapA wrong answer can be relevant but still not justified.

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.

Weak answer

Omar must have a school badge.

Strong answer

Only-if means badge -> completed log. Leila has the badge, so her log completion is forced; Omar may or may not have the badge.

First move

Weaker: Looks for a familiar word or number.Stronger: Uses the conditional reasoning routine.The routine keeps the answer tied to evidence.

Proof

Weaker: Gives a plausible answer without a clear link.Stronger: Shows how the stated information supports the answer.Reasoning questions reward justified conclusions.

Trap control

Weaker: Treating 'if P then Q' as though it also says 'if Q then P'.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.

If a code starts with R, it must be checked twice. Code R47 starts with R. What follows?

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  • Translate if, only if, all, none and unless into usable rules.
  • Use the contrapositive when it is valid.
  • Avoid the converse and inverse traps.