Chapter 9: Propositions and their Converses - Solutions
Chapter solutions are on NCERT Archive
Step-by-step solutions for this chapter now live on NCERT Archive, along with the chapter itself. Use the buttons below to open them.
About Chapter 9 (Propositions and their Converses)
Chapter 9 (Propositions and their Converses) is chapter 9 of 14 in the new edition of Ganita Manjari (NCERT Class 9 Mathematics), a textbook for Class 9 students at the Secondary stage. This is the new edition, the textbook brought out under the NEP 2020 / NCF-SE 2023 syllabus rollout.
Chapter 9 introduces propositions (statements that are true or false) and their converses. Through everyday examples and results from number theory and geometry, such as multiples of 6 and 3, perfect squares and odd numbers of factors, and the Baudhayana-Pythagoras theorem, it shows that a proposition can be true while its converse is false, that both can be true, or that both can be false. It also shows how a counterexample is used to disprove a statement.
In the book it comes after Chapter 8 (Predicting What Comes Next: Exploring Sequences and Progressions) and before Chapter 10 (How Quantities Combine: Understanding Data), so it helps to be comfortable with the earlier chapters before starting it.
Topics covered
- Propositions and 'if X then Y' statements
- The converse of a proposition
- Counterexamples
- Perfect squares and the number of factors
- Converse of the Baudhayana-Pythagoras theorem
What the solutions on NCERT Archive include
NCERT Archive is our dedicated site for NCERT textbooks and solutions, Class 1 to 12. The solutions page for Chapter 9 (Propositions and their Converses) there gives chapter-wise answers to the questions of Ganita Manjari (NCERT Class 9 Mathematics), written to follow the order of the textbook, and links back to the chapter itself. Use the buttons above to go to it.
How to study Propositions and their Converses
- Read the worked examples before the exercises and copy out each step in your own hand.
- Attempt every exercise question yourself first; open the solution only to check your method or when you are stuck.
- Keep a short list of formulas and definitions from the chapter and revise it before tests.
- Redo the questions you got wrong after a day or two, without looking at the solution.
Frequently Asked Questions
Which book is Chapter 9 (Propositions and their Converses) of Class 9 Mathematics from?
It is from the new edition of Ganita Manjari (NCERT Class 9 Mathematics). The book has 14 chapters, and this is chapter 9.
Where can I find the solutions for Chapter 9 (Propositions and their Converses) of Class 9 Mathematics?
On NCERT Archive. Press the "Open Chapter Solutions" button on this page and you will land on the solutions page for this chapter there.
Is this the new edition or the old edition?
This page is for the new edition. If your school still uses the earlier textbook, use the Old Edition switch at the top of the page.
Is it free to use?
Yes. Scholar Donkey and NCERT Archive are free to use and need no login.