Problem 1: A variable in a lambda calculus expression can be bound to one of the X terms, or is free if it isn't bound to any. (Refer to Section 1.1 of the lambda calculus tutorial written by R. Rojas for additional explanation.) For each of the following expressions, identify which variables are bound and which are free: (a): (ax.x) (b): (Qx.x) y (c): (axy.xz) y (d): (ax.x) Qy.yx) Hint: There may be more than one distinct variable named 'x'. y'. or z' in a given expression! When there is, clarify which variable you're referring to, e.g. "the x inside the first lambda is bound" Problem 2: For each of the expressions in Problem 1, show what it reduces to. (If an expression doesn't reduce any further, just write the expression as-is as your answer.) Hint: You are allowed to, and probably should, use an interpreter such as the one at http:lljacksongl.github.iolfiles/demollambda/