1) What is a semantic tableau and what is the main advantage of using it to determine if a formula is satisfiable? - Theorem 2.60 in our textbook states: A set of literals is satisfiable if and only if it does not contain a complementary pair of literals. Discuss and illustrate with examples the meaning of this theorem. (note: a literal is a propositional variable or a negation of a propositional variable) 2) Discuss the algorithm for the construction of a semantic tableau for a formula in propositional logic. What is the main idea of the algorithm? - Show and discuss examples of the use of semantic tableaux.

3)Consider the following sentence: Let A and B be arbitrary formulas. If A and B are logically equivalent then A <-> B is a tautology. Is that correct? Why? How about the converse? 4)The Lecture Notes given for this module provides a list of logical equivalences and call them algebraic laws of the propositional logic. Why call them like that? 5) How can we demonstrate or prove the laws of the propositional logic? Please illustrate with one example. 6) What do you understand by simplification of a propositional formula? Show an exampl