Proofs & Logic — How We Know
Direct proof & counterexamples
continues from lesson 2 — values defined earlier in the course stay live here
ELI5: a direct proof argues straight from definitions: "the sum of two even numbers is even" because 2a + 2b = 2(a + b), which is divisible by 2. The opposite tool is the counterexample — a single case that demolishes a universal claim. "All primes are odd" dies the instant you remember 2.
✓ pass even + even is even (a concrete instance of the proof)
✓ pass 2 is an EVEN prime — the counterexample to "all primes are odd"
Real-world hook: finding one counterexample is how bugs are reported and how security flaws are demonstrated — a single failing case is enough to disprove "it always works."