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Definitions and axioms of logic

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

Definitions

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

Axioms

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

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