# Definitions and axioms of logic

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The undefined terms in logic are **statement**, **true**, and **false**.

## Definitions

- An
**axiom**is a statement that is accepted to be true without proof. - A
**proof**is a logical argument made to verify the truth of a statement. - A
**theorem**is a statement that has been demonstrated to be true by method of proof. - A
**lemma**is a theorem that is used in a proof of another theorem. - A
**corollary**is a result that follows quickly from a theorem. - A
**claim**is a minor statement that is to be proven within a proof of another theorem. - A
**conjunction**is a statement of the form, where*P*and*Q**P*and*Q*are the component statements. - A
**disjunction**is a statement of the form, where**P or Q***P*and*Q*are the component statements. - A
**conditional statement**is a statement of the form**If**, where*P*, then*Q**P*and*Q*are the component statements. - A
**biconditional statement**is a statement of the form, where*P*, if and only if*Q**P*and*Q*are the component statements.

## Axioms

- Any statement is either true or false, but not both true and false.