Question: FORMAL LOGIC Computer Science School of Computing 1.3 Show that the formula in Question 1.2 is a theorem of the Gentzen system G. Annotate the

FORMAL LOGIC

Computer Science School of Computing

1.3 Show that the formula in Question 1.2 is a theorem of the Gentzen system G. Annotate the lines of your proof with the rules used. (i) Define the satisfiability and unsatisfiability of a set of formulas. (ii) Consider the following theorem: If U=A then U{B}=A for any formula B. Say U is a satisfiable set of formulas, but B is an unsatisfiable formula. Will U{B} not then be an unsatisfiable set, and does this not show that the theorem is incorrect? Explain your answers, referring to the definitions of satisfiability and unsatisfiability of a formula and a set of formulas

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