Select the true statements: F. In a structural induction proof, to show that a s

Question

Select the true statements:

F. 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.
G. 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.
H. You can prove a statement P(n) for all natural numbers n by showing P(1) and P(n)P(n+1)P(n)P(n+1) for all natural numbers n.
I. Induction is a special case of structural induction.
J. 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.

Explanation / Answer

F is true , For eg in structural induction if we want to prove that a entire population has a trait , then we have to prove it for initial population and then to prove that it is transmitted to all direct descendents ie it pass through all the element in creating a new element from the old.

G is true , since in mathematical induction , first we check for n=1, then y assuming for n , we prove for n+1

H is false,

I is true since induction is a special case of structural induction

J is false

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.