🧠 Logic & Proofs Without the Misery

🧠 Logic & Proofs Without the Misery

Put n = 0, 1, 2 and so on into n² + n + 41 and you get a prime number every time, forty times in a row. At n = 40 the answer is 1,681, which is 41 × 41. A pattern that held forty times was never a rule. This book shows how mathematicians know something is true forever, not just true so far.

WHAT'S INSIDE:

💬 Statements — sentences that are either true or false, with no in-between

📋 And, or, not — truth tables, and the inclusive "or" that math always means

🌧️ If-then — the converse and the contrapositive, and why a wet ground doesn't prove it rained

🌍 Quantifiers — "for all" and "there exists", and how to negate them correctly

➡️ Direct proof — from what you know to what you want, one step at a time

💥 Proof by contradiction — assume the opposite and watch it fall apart

⛓️ Proof by induction — the domino method that proves a formula for every whole number

🔨 Counterexamples and fallacies — why one counterexample beats a million examples

⚠️ A "5 Common Mistakes" chapter — including treating examples as a proof

🧮 A Logic Rules & Quick Reference appendix, with a worked example

✏️ 10 fully worked examples with every step shown

✅ 11 practice problems with complete answers at the back

WHO THIS IS FOR:

Anyone who watched a proof in class and felt the teacher already knew the ending. Anyone starting university math who needs to read and write proofs.

No prior knowledge of proofs required. 22 pages.