Problem 3 Programming in Lambda Calculus In lecture 19 and 20, we discussed the encoding of logical constants true and false in lambda calculus, together with the implementation of logical operators.

1. Compute the value of ((and true) true) using ?-reductions.

2. Define the or operator in lambda calculus. Prove that your definition is correct, i.e., your lambda term for or implements the logical or operation.

3. Define the exor (exclusive or) operator in lambda calculus. Prove that your definition is correct, i.e., your lambda term for exor implements the logical exor operation.