A conditional statement is an if-then statement: if p, then q. Learn its two parts (hypothesis and conclusion), when it is true, and how to form its converse, inverse, and contrapositive, with geometry examples.
What a conditional statement is
A conditional statement is an "if-then" statement: it claims that if one thing is true, then another thing follows. In geometry and logic it is written "If p, then q." These statements are the backbone of reasoning and proof, and they build on simpler statements.
A conditional statement has the form "if hypothesis, then conclusion."
Hypothesis and conclusion
Every conditional has two parts. The hypothesis is the "if" part — the condition. The conclusion is the "then" part — what follows. In "If a shape is a square, then it has four sides," the hypothesis is "a shape is a square" and the conclusion is "it has four sides."
When a conditional is true
A conditional statement is considered false only in one case: when the hypothesis is true but the conclusion is false. In every other case it counts as true. So "If it rains, then the ground gets wet" is only broken by a day when it rains and the ground somehow stays dry.
Converse, inverse, and contrapositive
From any conditional you can build three related statements by swapping and negating its parts. Negating uses negations (the "not" of a statement).
The four forms: conditional, converse, inverse, and contrapositive.
Converse: swap the parts — "If q, then p."
Inverse: negate both parts — "If not p, then not q."
Contrapositive: swap and negate — "If not q, then not p." It is always equivalent to the original.
The converse and inverse are not automatically true just because the conditional is. For a full treatment, see converse, inverse, and contrapositive.
Examples
Conditional: "If a shape is a square, then it has four sides." (true)
Converse: "If a shape has four sides, then it is a square." (false — it could be a rectangle)
Contrapositive: "If a shape does not have four sides, then it is not a square." (true)