Select all true statements.


a. The rules that create new from old elements in a recursively defined set never create the same element twice.

b. In a structural induction proof, to show that a statement holds for all elements of a recursively defined set, you must show it for all members of the initial population, and that it is passed on through the recurrence relations that create new elements from old elements.

c. You can prove a statement P(n) for all natural numbers n by showing P(1) and for all natural numbers n.

d. In a structural induction proof, to show that a statement P(n) holds for all elements n of a recursively defined set, you must show P(n) for all n in the initial population, and that whenever P(n) is true for some n, P(n 1) is also true.

e. Induction is a special case of structural induction.