Direct Proof
📋 What it is
A direct proof assumes the “if” part and marches step by step straight to the “then” part.
🗣️ Coach says
Direct proof is the most straightforward tool: take what you’re given, use definitions and known facts, and walk directly to the conclusion. No tricks — just a clean path from start to finish.
🧠 Memory hook
Start at the “if”, walk straight to the “then”. Use definitions as stepping stones.
😂 Giggle
What's a logician's favorite dessert?
Proof pudding — because the proof is in the pudding!
😲 Whoa!
Most theorems you meet in school are proved directly — it’s the default technique, and the one the others fall back on.
✅ Quick check: To prove “if n is even then n² is even”, what’s a good first step?
Say your answer out loud first — then reveal.
Write n = 2k (the definition of even), then n² = 4k² = 2(2k²), which is even. Starting from the definition unlocks it.
A direct proof turns the hypothesis into usable form (a definition) and computes toward the goal.
🧪 Try it! (2 minutes)
Prove directly: “if you double any whole number, the result is even.” Start by writing the doubled number as 2 × (something).