Lambda calculus binding(State which variable is bounded to which abstraction) - Use the example below as a sample and answer the questions a-e.

Problem 2 (Lambda calculus binding). For each of the following determine for each variable x the Ax. 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. If variables 4 and 7 are bound to abstraction I, your answer should be of the form I 4, 7 to indicate that abstraction I has variables 4, and 7 bound by it. (2x, x x . x )x I1 2 11 34 Example 1,2 l 93 Answer a. x (x. x x)x 2x, (2x. (2x. x x(2x. x ) x) (2x. x x ) (2x. x ) )x IIIlI 1 2 IV 3 4V56VI 78 Problem 2 (Lambda calculus binding). For each of the following determine for each variable x the Ax. 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. If variables 4 and 7 are bound to abstraction I, your answer should be of the form I 4, 7 to indicate that abstraction I has variables 4, and 7 bound by it. (2x, x x . x )x I1 2 11 34 Example 1,2 l 93 Answer a. x (x. x x)x 2x, (2x. (2x. x x(2x. x ) x) (2x. x x ) (2x. x ) )x IIIlI 1 2 IV 3 4V56VI 78