The propositional formula (P -> Q) is logically EQUIVALENT to:
P -> Q is equivalent to both its disjunctive form (~P v Q) and its contrapositive (~Q -> ~P).
A propositional formula with n boolean variables has how many total distinct truth assignments?
With n binary variables, there are $2^n$ total rows in the truth table.
Which logic gate operator alone forms a functionally complete set for propositional logic?
NAND (and NOR) are universal gates capable of expressing all boolean functions without other operators.
In First-Order Logic, Skolemization converts existential quantifiers into:
Existentials outside universal scopes become Skolem constants; inside universal scopes they become Skolem functions.
In Resolution Refutation, proving that Knowledge Base KB entails sentence $\alpha (KB |= \alpha)$ is accomplished by showing that:
Resolution refutation negates the target sentence $\alpha$ and derives a contradiction (empty clause box) from KB ^ ~$\alpha$.