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.
Negating quantifiers and compound statements is one of the most important proof skills.
Rules:
Negations show up constantly in contradiction proofs.
TL;DR — key idea
Negations flip quantifiers and break apart logical structure using equivalence rules like De Morgan’s laws.
Don’t skip this – writing proofs or explanations on paper is where most of the learning actually happens.
Negate the following statements and simplify: 1. ∀x ∈ ℝ, x + 5 > 10 2. ∃n ∈ ℕ such that n is even and prime 3. If n is odd, then n² is odd Explain your reasoning clearly.
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.