How logical inference can be solved in Propositional Logic?

In propositional logic, logical inference is typically solved using various methods, including:

1. Truth Tables: One of the most straightforward methods is using truth tables to exhaustively enumerate all possible combinations of truth values for the propositional variables involved in the given statements. By systematically evaluating each combination, you can determine the truth value of the compound proposition in question.
2. Logical Equivalences: Exploiting logical equivalences such as De Morgan’s laws, double negation, distributive laws, etc., can help simplify complex expressions and facilitate the process of logical inference by transforming the original propositions into equivalent but more easily analyzable forms.
3. Rules of Inference: Propositional logic employs several rules of inference, such as modus ponens, modus tollens, conjunction elimination, disjunction introduction, etc. These rules provide systematic ways to derive new propositions from existing ones based on logical principles.
4. Semantic Tableaux (Truth Trees): Semantic tableaux provide a graphical method for testing the satisfiability of sets of propositional clauses. By systematically branching out and applying inference rules, you can determine whether a set of propositions is satisfiable or not.
5. Resolution: Resolution is a powerful inference rule used in automated theorem proving. It involves transforming a given set of propositions into clauses and then systematically applying resolution steps to derive new clauses until a contradiction (empty clause) is reached, indicating that the original set of propositions is unsatisfiable.

Each of these methods has its strengths and weaknesses, and the choice of method often depends on the specific problem at hand and the computational resources available.