Theorems in propositional logic

property involving two mathematical operations

pair of transformation rules that are both valid rules of inference

logical principle stating that for every proposition, either it or its negation is true

form of argument in informal logic

theorem of logic

if X implies Y, and X is true, then Y is true

if X implies Y, and Y isn't true, then neither is X

In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as . The contrapositive of a statement has its antecedent and consequent negated and swapped.

in logic, rule of inference

theorem which states that any statement can be proven from a contradiction

term

inference rule in logics : with "A or B" and "not A" deduce "B"

Axiom used in logic and philosophy

theorem

theorem

inference in propositional logic

theorem

if X and Y can't both be true, and X is true, then Y isn't true

inference introducing a disjunction in logical proofs

property of many logical systems that if a sentence follows deductively from a given set of sentences then it also follows deductively from any superset of those sentences

rule of inference of propositional logic

theorem

metatheorem that states that the Peano axioms of arithmetic can be derived in second-order logic from Hume's principle

Rule of inference of propositional logic

inference rule where, given P→Q, one deduces P→(P∧Q)

ancient French logician

Rule of inference of propositional logic

Inference in propositional logic