COMPARE — Proposition and Converse Together

02 · UNDERSTAND

Proposition and Converse Together

Judge the proposition and its converse separately. We study true/false, true/true and false/false pairs. These are not the only possible arrangements; a false proposition can have a true converse.

03 · KEY IDEAS

Keep the conditions clear.

• Each true direction needs a reason.
• Each false direction needs its own valid counterexample.
• Changing the starting direction exchanges the two verdicts.

04 · VISUALISE

Follow the direction.

06 · ORIGINAL AIMS WORKED EXAMPLE

Follow each step.

For positive integers, compare “multiple of 4 implies multiple of 10” and its converse.

1. 4 is a multiple of 4 but not of 10: the original is false.
2. 10 is a multiple of 10 but not of 4: the converse is false.
3. A shared multiple such as 20 supports both statements in one case but proves neither universal claim.

07 · AIMS METHOD

Your turn to reason.

1. AAttempt independently
2. IInvestigate the idea
3. MMake connections
4. SScrutinise your reasoning

Can a proposition be false while its converse is true?

08 · PRACTICE SPRINT

Use the idea in a new situation.

Ten original AIMS questions: 3 Warm-up, 4 Build, 2 Think and 1 Challenge.

Check & Feedback: incorrect answers receive a conceptual hint and another attempt; correct answers include reasoning.

TEXTBOOK CONNECTION

Return to the source. Bring your reasoning.

Ganita Manjari · Grade 9 · Part II · Chapter 9. Use your textbook for the complete questions. These are topic references and original AIMS guidance, not reproduced exercises.