1. (Lambda calculus: binding). For each of the following expressions. determine for each variable x the ex. it is bound to. I have numbered the variables and the abstractions. The variables are numbered using Arabic numerals and the abstractions are numbered using roman numerals and you should specify which variable numbers are bound to which abstraction number. For example, if variables 4 and 7 are bound to abstraction I, your answer should be of the form 1 + 4 7 to indicate that abstraction ! has variables 4, and 7 bound by it. If variable 3 is free, then your answer should have the form free +3. Example Answer (Ay x yax, y ) i 1 2 11 3 4 free - 4 1 11 Your answers need not be colored L1, Ay. X Y Z 1 1 2 3 1.2. Ax. x y (Az. y Cay. 2) X II 2 1 3 4 5 1.3. ( . x . xy ax. 12 11 3 11 4 5 IV 6 7 8 1.4. (ax. y ly. x ) ( Ax. ix. xxix. x )x) 1 ili 2 3 III IV 45 V 6 7 8 1.5. ix. y ay. X X (Ax. ix. (x x) ly. x ))x 1 2 3 III IV 4 SV 6 7 8