STATE — Concept Note

Concept

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.

Key Ideas

• 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.

Rule / Property

Read the whole sentence. Ask whether it states something, then decide whether there is enough information to judge it. Classify before deciding truth.

Visual Recall

1. Read the condition
2. → Check the direction
3. → Justify the conclusion

Mini Example

Classify “27 is a multiple of 4”, “Find a multiple of 4” and “27 +”.

The second is an instruction; the third is unfinished. Neither has a truth value.

Common Mistake

Calling a false statement “not a proposition”. Falsity is a truth value.

Quick Recall

Is “Every square has five sides” a proposition?