NCERT Solutions Class 9 Maths Chapter 9 — Propositions and their Converses#
Chapter 9 (Ganita Manjari Part II) is about propositions — statements that are either true or false — and their converses. A proposition of the form “if X then Y” has the converse “if Y then X”. You will see that a true proposition can have a false converse, and learn to disprove a statement with a single counterexample.
Exercises#
- Exercise Set 9.1 — Converses in geometry and number theory, counterexamples to prime-generating formulas, divisibility tests, and choosing diagonals for a quadrilateral (17 questions)
What you will learn#
- Propositions and ‘if–then’ statements.
- Writing the converse of a statement and deciding whether it is true.
- Proving statements, and disproving them with a counterexample.
- Examples from geometry, divisibility tests and prime-generating formulas.
Key formulas and results#
- The converse of ‘If P, then Q’ is ‘If Q, then P’.
- One counterexample is enough to show that a general statement is false.
Read and revise#
- NCERT Class 9 Maths Chapter 9 (PDF) — the Ganita Manjari Part II chapter itself.
- All Class 9 Maths chapters from Ganita Manjari Part I and Part II.
Frequently asked questions#
How many exercises are in Class 9 Maths Chapter 9?
One exercise set — 9.1 (17 questions). Every question is solved step by step here.
Is the converse of a true statement always true?
No. ‘If a number is divisible by 4, it is even’ is true, but its converse, ‘If a number is even, it is divisible by 4’, is false: 6 is even but not divisible by 4.