Problem 3 (lambda calculus Beta Reductions). For each of the following expressions, give the resulting expression after executing a beta reduction of the highlighted redex. Examples are shown below 1. Do renaming only if needed. You should not do renaming if it is not needed Do not forget to add parentheses when t' is an non-parenthesized abstraction. The bound variables of the redex are identified for you in parts a. and b. You should identify the bound variabbles in parts c. and d. as part of your answer 2. 3. a. (2x. xyx) y. yy (Ax. t t' (Ax. (2x. (2y Example 1: for the expression (Ax. t ) t, your answer should be (Jx. x ) (2x. x x) // beta reduction Example 2: for the expression (Xx. your answer should be // renaming // beta reduction Problem 3 (lambda calculus Beta Reductions). For each of the following expressions, give the resulting expression after executing a beta reduction of the highlighted redex. Examples are shown below 1. Do renaming only if needed. You should not do renaming if it is not needed Do not forget to add parentheses when t' is an non-parenthesized abstraction. The bound variables of the redex are identified for you in parts a. and b. You should identify the bound variabbles in parts c. and d. as part of your answer 2. 3. a. (2x. xyx) y. yy (Ax. t t' (Ax. (2x. (2y Example 1: for the expression (Ax. t ) t, your answer should be (Jx. x ) (2x. x x) // beta reduction Example 2: for the expression (Xx. your answer should be // renaming // beta reduction