Using mathematical logic, with variables. Question of theoretical computing.

4. For a natural number n we recursively define the factorial of n as following: i, 20 n! In(n-1)...1, for n > 1. (a) (10 points) Define the factorial function for a natural number n recursively as a lambda function. (b) (10 points) Define the factorial function for a natural number n recursively as a primitive recursive function