Class 09 | Ganita Manjari 02 | Ch. 09 Propositions and their Converses | Solutions
Class 09 | Ganita Manjari | Part II | Ch 09: Propositions and their Converses | Solutions ๐ Ganita Manjari | Part II CBSE 2026-27 Key Concepts at a Glance ★ A proposition is a statement that is either true or false (never both). ★ Many propositions have the form "if X then Y", also written "X implies Y", or "Y when X" — all three mean the same thing. ★ The converse of "if X then Y" is "if Y then X" — the two parts swap places. ★ A proposition being true tells you nothing about whether its converse is true. Any combination can happen: both true, only one true, or both false. ★ A counterexample is a single example that satisfies X but not Y — one is enough to prove "if X then Y" is false. ★ To prove a proposition true, you need an argument that works for every case — checking a few examples is never enough. ★ When a proposition and its converse are both true, X and Y "imply each other" (e.g. ...