MASTER — Concept Note

Concept

Bring the chapter together: read a claim, identify its direction, test its logic and conclude with a reason or a counterexample. Use the mastery work to identify what needs another look, not to guess a label.

Key Ideas

• A correct converse preserves every condition.
• One valid counterexample defeats a universal claim; examples alone do not prove one.
• Number, figure and proof questions all need explicit reasons.

Rule / Property

Read the claim → identify the direction → test the logic → justify or counterexample → conclude.

Visual Recall

1. Read the condition
2. → Check the direction
3. → Justify the conclusion

Mini Example

A learner claims that a number with exactly four positive factors must be a product of two distinct primes.

Verify: a product pq of distinct primes does have four factors, 1, p, q, pq; this true direction does not prove the reverse.

Common Mistake

Confusing “I have not proved it” with “it is false”, or accepting a conclusion before checking its conditions.

Quick Recall

What must accompany a false verdict?