# Implication & Conditionals

"If it rained, the street is wet." Simple sentence - and the source of more bad reasoning than almost
anything else in logic. From it, people wrongly conclude "the street is wet, so it rained" (a sprinkler
would like a word). That slip has a name, it's everywhere, and once you can spot it you'll see it in
arguments, in contracts, and in your own code.

This guide is about the conditional - *if P then Q* - the connective important enough to earn its own
guide separate from [Propositional Logic](/guides/propositional-logic). We'll pin down exactly when it's
true (the part that surprises everyone), map the four ways people flip it around and which flips are
legal, and settle the necessary-versus-sufficient confusion that trips up even experienced engineers.

## How to read this
- **Want the one big fix?** [Phase 2](02-converse-inverse-contrapositive.md) is the "the street is wet
  so it rained" mistake, dismantled for good.
- **Want the whole picture?** Read in order - Phase 1 builds the foundation the other two stand on.

## The phases
1. **[What "If P Then Q" Really Means](01-what-if-p-then-q-means.md)** - the truth table of implication,
   and why a conditional is only false in one specific case.
2. **[Converse, Inverse, Contrapositive](02-converse-inverse-contrapositive.md)** - the four forms, the
   one that's equivalent, and the two classic errors that fool everybody.
3. **[Necessary vs Sufficient Conditions](03-necessary-and-sufficient.md)** - the distinction that makes
   requirements, validation, and "if and only if" finally make sense.

> This completes the core of how statements connect. The Logic track continues into quantifiers
> ("for all" / "there exists"), proof, and spotting fallacies.