REVERSE — Concept Note

Concept

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”.

Key Ideas

• 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.

Rule / Property

Name the starting condition P and the conclusion Q. Exchange them. Test the new direction independently.

Visual Recall

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

Mini Example

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

The value 2 is even but is not a multiple of 14. The converse is false.

Common Mistake

Adding “not” or changing the numbers instead of exchanging the two conditions.

Quick Recall

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