REVERSE — Understanding the Converse

02 · UNDERSTAND

Understanding the Converse

An if–then proposition has a starting condition and a conclusion. To form its converse, exchange those two parts and keep their meanings and domain unchanged. “P implies Q” has the same direction as “If P, then Q”.

03 · KEY IDEAS

Keep the conditions clear.

• Original: If P, then Q. Converse: If Q, then P.
• Reversing the arrow does not prove the reversed statement.
• “Q when P” still starts from P; it is not the converse.

04 · VISUALISE

Follow the direction.

06 · ORIGINAL AIMS WORKED EXAMPLE

Follow each step.

For positive integers: if n is a multiple of 14, then n is even.

1. Write n = 14k = 2(7k), so the original is true.
2. Converse: if n is even, then n is a multiple of 14.
3. The value 2 is even but is not a multiple of 14. The converse is false.

07 · AIMS METHOD

Your turn to reason.

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

Reverse “If a shape is a square, then it is a rectangle”.

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.