Select all true statements. you prove a statement P(n) by induction for all natu

Question

Select all true statements. you prove a statement P(n) by induction for all natural numbers n by showing P(1) and by showing that if P(k) is true for all natural numbers k, then P(k+1) must also be true. you can prove a statement P(n) for all natural numbers n by showing P(1), P(2) and P(n) rightarrow P(n + 1) for all natural numbers n. Induction is a special case of structural induction. 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. The Fibonacci sequence f_n is big-Omega of (3/2)^n. you can prove a statement P(n) for all natural numbers n by showing P(1) and P(n) rightarrow P(n + 1) for all natural numbers n. If P(n) is a statement that is false for some, or even all, natural numbers n, it is still possible that P(n) rightarrow P(n + 1) holds for all natural numbers n. 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. The rules that create new from old elements in a recursively defined set never create the same element twice. in an inductive proof, you always obtain the statement P(n+1) by adding n to both sides of P(n).

Explanation / Answer

A) True.(by definition)

B) True.(by definition)

C) False (because in structural induction,we can prove statements which are recursively defined,and more convenient form of induction.But our concept is from induction.by structural induction,you can easily do proofs.

D)TRUE(By definition of structural induction)

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