GANITA MANJARI · GRADE 9 · PART II · CHAPTER 9
TEST — Concept Note
Think first. Use AI purposefully. Verify always.
Concept
A counterexample satisfies the starting condition but fails the conclusion. One such example disproves an “always” claim. Many successful checks do not prove every possible case.
Key Ideas
- Check that your example belongs to the stated domain.
- A supporting example does not disprove a claim.
- Not finding a counterexample is not the same as proving the claim.
Rule / Property
Read the claim → think → choose a permitted example → check the condition → test the conclusion → conclude.
Visual Recall
- Read the condition
- → Check the direction
- → Justify the conclusion
Mini Example
Claim: every positive multiple of 7 is odd.
14 is even, so the conclusion fails. The claim is false.
Common Mistake
Using a value that fails the starting condition, or treating five successful tests as a proof.
Quick Recall
Why does 18 disprove “Every multiple of 3 is a perfect square”?
Check your reasoning
18 = 3 × 6 but lies strictly between and , so it is not a square.