COMPARE — Concept Note

Concept

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.

Key Ideas

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

Rule / Property

Write both directions side by side. For each, give a general reason or a counterexample before naming the pair.

Visual Recall

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

Mini Example

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

A shared multiple such as 20 supports both statements in one case but proves neither universal claim.

Common Mistake

Using the same verdict for both directions without checking each.

Quick Recall

Can a proposition be false while its converse is true?