Suppose f1f2gcis a first-order language where f1, f are binary function symbols, g is a unary function symbol, is a binary predicate symbol, and c is a constant symbol. Consider the usual structure of the number theory as an -structure =N, +, S<, 0 by the following interpretations: f is + (the addition function, f is the multiplication function, g is S the successor function, is < the usual order relation, and is the number 0.
(a) What is the interpretation of the term f1ggcf2gyin, where x is 2 and y is 3? Show your work.
(b) Find the value of the A where A is the C-formula xVyf2xy=y.
(c) Write an C-formula B with a free variable such that =Bmiff m is an odd number.