Solve the lambda calculus question:

For each of the following pairs of λ-terms, say whether or not they are equivalent. If they are, give the steps with what kind of equivalence/reduction you’re using.

For example, if the question is (λx.λy.x y) λz.z ? ≡ λu.(λv.(λz.z) v) u you could write (λx.λy.x y) λz.z ≡β λy.(λz.z) y ≡α λv.(λz.z) v ≡η λu.(λv.(λz.z) v) u

(a) x ? ≡ z

(b) (λy.λz.y) x ? ≡ λy.x

(c) x ? ≡ λx.x x

(d) λy.x ? ≡ (λz.λy.x) z

(e) λy.x ? ≡ λz.(λy.x) z