Could someone expound on one of the following?

- Consider the following sentence: Let A and B be arbitrary formulas. If A and B are logically equivalent, then A B B is a tautology. Is that correct? Why? How about the converse? - 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? - How can we demonstrate or prove the laws of the propositional logic? Please illustrate with one example. - Discuss an example in which one or more logical equivalences are used to simplify a propositional formula