GANITA MANJARI · GRADE 9 · PART II · CHAPTER 9
STATE — What Is a Proposition?
Think first. Use AI purposefully. Verify always.
01 · DISCOVER
Start by thinking.
Compare “14 is even”, “Is 14 even?” and “Divide 14 by 2”. Which says something that can be judged true or false?
Try 1 of 3: “26 is a multiple of 3.”
Classify first.
02 · UNDERSTAND
What Is a Proposition?
A proposition makes a complete statement with a truth value. It can be true or false: being false does not stop it being a proposition. A question asks for information; an instruction asks for an action. An expression alone does neither.
03 · KEY IDEAS
Keep the conditions clear.
- A complete statement can be tested as true or false.
- Questions, commands and unfinished expressions are not propositions.
- An unspecified variable may leave a statement incomplete: state the value or the condition first.
04 · VISUALISE
Follow the direction.
Complete statement → proposition → judge true or false. A question or instruction follows a different path.
05 · METHOD / REASONING
Make the argument checkable.
Read the whole sentence. Ask whether it states something, then decide whether there is enough information to judge it. Classify before deciding truth.
06 · ORIGINAL AIMS WORKED EXAMPLE
Follow each step.
Classify “27 is a multiple of 4”, “Find a multiple of 4” and “27 +”.
- The first is a complete statement: it is a proposition.
- Since 27 = 4 × 6 + 3, that proposition is false.
- The second is an instruction; the third is unfinished. Neither has a truth value.
07 · AIMS METHOD
Your turn to reason.
- Attempt independently
- Investigate the idea
- Make connections
- Scrutinise your reasoning
Is “Every square has five sides” a proposition?
Compare after your own attempt
Yes, a false proposition. A square has four sides.
08 · PRACTICE SPRINT
Use the idea in a new situation.
Ten original AIMS questions: 3 Warm-up, 4 Build, 2 Think and 1 Challenge.
Start Practice Sprint →Check & Feedback: incorrect answers receive a conceptual hint and another attempt; correct answers include reasoning.
TEXTBOOK CONNECTION
Return to the source. Bring your reasoning.
Ganita Manjari · Grade 9 · Part II · Chapter 9. Use your textbook for the complete questions. These are topic references and original AIMS guidance, not reproduced exercises.
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