If you prove by strong induction a statement of the form ∀ n ≥ 1P(n), the...

If you prove by strong induction a statement of the form ∀ n ≥ 1P(n), the inductive step proves the following implications (multiple correct answers are possible):

a) (P(1) ∧ P(2)) => P(3)

b) (P(1) ∧ P(2) ∧ P(3)) => P(4)

c) P(1) => P(2)

Expert Solution

To answer this first we have to know the difference between general induction and strong induction .

In general induction , we prove the induction step that is to prove the statement for we have the induction hypothesis the statement is true for .

While in strong induction we prove the induction step that is to prove the statement for we have the induction hypothesis the statement is true for , or more values of

That is if we assume that the statement is true for to prove that the statement is true for then it is general induction and if we assume more values of to prove that the statement is true for then it will be strong induction .

Hence ,

is strong induction .

is not strong induction .

Answer : and .

.

If you have any doubt please comment .

Colby Messinger answered 2 years ago

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Question

If you prove by strong induction a statement of the form ∀ n ≥ 1P(n), the...

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Expert Solution

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