Intro to Proofs

Proposition

A statement that is either true or false

A proposition whose truth depends on the value of one or more variables

Predicate

A proposition that is simply accepted as true

Axiom

A sequence of logical deductions from axioms and previously proved statements that concludes with the proposition in question

Proof

An important true proposition

Theorem

A preliminary proposition useful for providing later propositions

Lemma

A proposition that follows in just a few logical steps from a theorem

Lemma

What is a proposition of the form IF P, THEN Q called?

Implication

What is the inference rule: P, P IMPLIES Q/ Q called?

Modus Ponens

What is the statement above the line in Modus Ponens called?

Antecedent

What is the statement below the line in Modus Ponens called?

Conclusion/consequent

Contrapositive of P IMPLIES Q

NOT(Q) IMPLIES NOT (P)

End of proof delimiter and symbol

QED, 🔲