Propositions, Statements, and Connectives

Read the explanation, try the on-paper prompts, then explain the idea in your own words. Use AI feedback as a mentor, not a shortcut.

10–20 min focusProof-first mindset

Best flow: read → think on paper → write a short explanation → refine with feedback.

Reading

Core explanation

Logic is the language of proofs. Every proof is really a chain of logical statements.

A proposition is a declarative statement that is either true or false, but not both. Examples:

"7 is prime." (true)
"5 > 10." (false)
"x > 2" is not a proposition unless x is specified.

Logical connectives combine statements:

¬P : NOT P
P ∧ Q : P AND Q
P ∨ Q : P OR Q (inclusive)
P → Q : IF P THEN Q
P ↔ Q : P if and only if Q

Understanding these connectives is essential because proofs manipulate statements using logical rules.

TL;DR — key idea

A proposition is a statement with a definite truth value. Logical connectives allow us to combine them into more complex statements.

Try these in your notebook

Don’t skip this – writing proofs or explanations on paper is where most of the learning actually happens.

1
Explain in your own words the difference between a statement and a non-statement. Then classify each item as a proposition or not: 1. "Every even number greater than 2 is prime." 2. "x + 3 = 9" 3. "This sentence is false."

Once you’ve sketched some ideas, summarize the main insight in the reflection box on the right.

Check your understanding

In 3–6 sentences, explain the core idea of this subsection as if you were teaching a friend who hasn’t seen it. Focus on the logic, not just the final statements.

AI is optional. Use it to spot gaps and sharpen your wording, not to replace your own thinking.