Use structural induction on terms and formulas to dene a function C that maps every term/- formula to the number of occurrences of free variables. For example, C(x.P(x,x,y,y,z)) = 3 because the argument has 2 free occurrences of y and 1 of z.

Hint: Use an auxiliary function C(V,A) that takes the set V of bound variables and a term/formula A. Dene C by structural induction on A. Then dene C(A) = C(, A).

Problem 9.2 (Induction) Use structural induction on terms and formulas to define a function C that maps every term/- formula to the number of occurrences of free variables. For example, C(Vx.P(x,x,y, y, z)) = 3 because the argument has 2 free occurrences of y and 1 of z. Hint: Use an auxiliary function C'(V, A) that takes the set V of bound variables and a term/formula A. Define C' by structural induction on A. Then define C(A) = C'(0, A)