Proofs & Logic — How We Know
Implication, converse & contrapositive
continues from lesson 1 — values defined earlier in the course stay live here
ELI5: "if P then Q" is the shape of every theorem. Two cousins to keep straight:
- the contrapositive "if not Q then not P" is always equivalent — same truth.
- the converse "if Q then P" is a different claim and often false.
Example: "if n is divisible by 4, then by 2" is true; its converse "divisible by 2 ⇒ divisible by 4" is false — 6 breaks it.
✓ pass the implication: 12 ÷ 4 ⇒ 12 ÷ 2
✓ pass the converse fails: 6 is divisible by 2 but NOT by 4
Real-world hook: mixing up a statement with its converse is the most common reasoning bug there is — "all fraud looks unusual" does not mean "all unusual activity is fraud."