Use both normal order reduction and applicative order reduction to reduce the following lambda expressions. Reach a normal form representation if possible. (10 %)

a) (λb . b 8) (λx . (add x 5))

b) (λa . (λb z . z b) a) p (λa . a)

c) (λx . x x x) (λx . x x x)

d) (λx . λy . (add x ((λx . (sub x 4)) y))) 8 9

e) (λc . c (λx . λb . b)) ((λx . λb . λf . f x b) p q)