Lesson subsection
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.
Best flow: read → think on paper → write a short explanation → refine with feedback.
Students often misunderstand the implication P → Q. It does not mean P "causes" Q.
It simply means: if P is true, then Q must also be true.
The only time P → Q is false is when P is true and Q is false.
An if and only if statement (P ↔ Q) means:
IFF statements are very common in definitions.
TL;DR — key idea
Implications are only false when the hypothesis is true and the conclusion is false. IFF means two statements imply each other.
Don’t skip this – writing proofs or explanations on paper is where most of the learning actually happens.
Give an example of a true implication and explain why it is true. Then give an example of a statement that is true "if and only if" and explain both directions.
Once you’ve sketched some ideas, summarize the main insight in the reflection box on the right.
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.