Recall that a set is considered to be a group relative to a binary function f and an object e if and only if: f is associative; e is an identitiy element for f, that is for any x, f(e,x) = f(x,e) = x; and every element has an inverse, that is, for any x, there is an i such that f(x, i) = f(i,x) = e. a) Formalize these as sentences of FOL with two nonlogical symbols, a function symbol f, and a constant symbol e, and show using interpretations that the sentences logically entail the following property of groups: For every x and y, there is a z such that f(x,z) = y b) Repeat the entailment proof using Resoulution. To do so, you will need to treat equality as a predicate and add to the sentences of part a) some or all of the axioms of equality: Reflexibility, symmetry, transitivity. In addition, add the axiom of the substitution of equals for equals, that is for every x, y and z, if x = y, then f(x,z) = f(y,z) and f(z,x) = f(z,y)