CBSE · Class 6-12

Class 9 · Ganita Manjari

Unit 9 · Class 9Ganita Manjari

Propositions and their Converses

What is a statement, when is it true, and how does a converse behave differently?

Lessons

3 concepts

1
What Counts as a Proposition
" $7$ is prime" is a proposition (true). " $x$ is even" is not — it depends on $x$ . Sentences that are opinions or questions are not propositions.
2
Conditionals and their Converses
The statement "If it rains, the ground is wet" is very different from its converse "If the ground is wet, it rained" — someone could have watered the garden. In maths this matters: the converse of a true theorem is not a…
3
Contrapositive and Proof by Contradiction
$p \Rightarrow q$ is equivalent to $\neg q \Rightarrow \neg p$ . Many number-theory proofs use the contrapositive because it's easier to argue about.

Skills to practise

Skill · medium

Propositions and their Converses — Practice