Show that the pure iteration scheme given in Definition 4.2 is equivalent to the primitive recursive scheme given in Definition 4.1. Indicate whether the following statements are true or false: a)...

Show that the pure iteration scheme given in Definition 4.2 is equivalent

to the primitive recursive scheme given in Definition 4.1.

Indicate whether the following statements are true or false:

a) All primitive recursive functions are total.

b) All total computable functions are primitive recursive.

c) All partial recursive functions are computable.

d) All total functions are computable.