3. 10 points total; each part 2.5 points Give a recursive definition of the set of free variables of a formula , i.e., those variables with at least one free occurrence in , as described in the video. To do so, fill in the question marks in the following template (note that we do not assume that the metavariables 'r' and 'y' refer to distinct variables, so you need to analyze the case where x = y and the case where x = y): (a) x is a free variable of P(y) iff ? (b) x is a free variable of -4 iff ? (c) for # E {A, V, +, }, x is a free variable of (# ) iff ? (d) for Q E {V, 3}, x is a free variable of Qyp iff ? 4. 10 points Given a model M = ( D, I), a subset A C D is said to be definable in the language of pure monadic predicate logic iff there is a pure monadic formula y with exactly one free variable x such that for some variable assignment g, A= {deD\\M gr:=d] 4}, i.e., A is exactly the set of objects d such that 4 is true under the variable assignment that maps x to d. For example, in the model in Figure 1, the set {2, 4} is defined by the formula -Sophomore(x). For every subset of the domain of that model, say whether it is definable by a formula or not. If it is definable, give a formula that defines it