In Propositional Logic, what is the truth table result of the material implication (P -> Q) when P is False and Q is False?
By the definition of material implication, P -> Q is False ONLY when P is True and Q is False. When the antecedent P is False, the implication is vacuously True.
Which classical rule of deductive inference derives conclusion Q directly from premises P and (P -> Q)?
Modus Ponens states: given P and P -> Q, infer Q. Modus Tollens infers ~P from ~Q and P -> Q.
Which classical rule of deductive inference derives conclusion ~P from premises ~Q and (P -> Q)?
Modus Tollens asserts: if P implies Q, and Q is false (~Q), then P must be false (~P).
What is Conjunctive Normal Form (CNF) in mathematical propositional logic?
CNF represents formulas as (L1 v L2 v ...) ^ (L3 v L4 v ...) ... where each bracketed clause is an OR of literals, joined by ANDs.
What is the transformation process called that eliminates existential quantifiers in First-Order Logic by substituting existential variables with functions of universally quantified variables?
Skolemization replaces existentially quantified variables with Skolem constants or Skolem functions depending on preceding universal quantifiers.