Area 1: What do we understand by "interpretation for a set of formulas"? Please provide examples. - Explain using examples what a satisfying interpretation of a set of formulas is. - What does U A mean? Provide examples of U and A where U A and U contains at least two formulas. - Why do we say that the definition of logical consequence is central to the formalization of logic deduction? - Discuss the formal concept of theory. - What do we understand by axiom?

Area 2:

What is a rule of inference? - What does the modus ponens rule of inference state? Illustrate with one or more examples the use of modus ponens. - What does the modus tollens rule of inference state? Illustrate with one or more examples the use of modus tollens. - Demonstrate with examples how we use the turnstile symbol. - Explain and illustrate one rule of inference (other than modus ponens and modus tollens).

Area 3:

What is a deductive system? What were they originally developed for? - What is the Hilbert deductive system? - What is the main difference between the Hilbert system and the Gentzen system? - Compare/contrast the way we prove theorems in math (formalized informal reasoning) versus proving theorems in a formal deductive system such as Hilberts. - Proofs in the Hilbert system could be elaborate; how can the process be simplified? - What is the importance of the deduction rule? - Explain with examples how the axioms of the Hilbert system are applied in proofs. - In the context of deductive systems, what do the following terms mean: consistency, independence, soundness, and completeness?