Suppose P(n) is the statement "n+1=n+2". What is wrong with the following "proof" that the statement P(n) is true for all nonnegative integers n: You assume that P(k) is true for some positive integer k; that is k + 1=k + 2. Then you add 1 to both sides of this equation to obtain k +2 = k +3; therefore P(k + 1) is true. By the principle of mathematical induction P(n) is true for all nonnegative integers n. O There is nothing wrong with this proof. O The proof is incorrect because you cannot add 1 to both sides of the equation in the inductive step. O The proof is incorrect because the statement used in the inductive hypothesis is incorrect. O The proof is incorrect because there is no basis step.

Suppose P(n) is the statement "n+1=n+2". What is wrong with the following "proof" that the statement P(n) is true for all nonnegative integers n: You assume that P(k) is true for some positive integer k; that is k + 1=k + 2. Then you add 1 to both sides of this equation to obtain k +2 = k +3; therefore P(k + 1) is true. By the principle of mathematical induction P(n) is true for all nonnegative integers n. O There is nothing wrong with this proof. O The proof is incorrect because you cannot add 1 to both sides of the equation in the inductive step. O The proof is incorrect because the statement used in the inductive hypothesis is incorrect. O The proof is incorrect because there is no basis step.

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Description: Suppose P(n) is the statement "n+1=n+2". What is wrong with the following "proof"that the statement P(n) is true for all nonnegative integers n:You assume that P(k) is true for some positive integer k; that is k +1= k +2. Then you add 1to both sides

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Suppose P(n) is the statement "n+1=n+2". What is wrong with the following "proof"
that the statement P(n) is true for all nonnegative integers n:
You assume that P(k) is true for some positive integer k; that is k +1= k +2. Then you add 1
to both sides of this equation to obtain k +2 =k + 3; therefore P(k + 1) is true.
By the principle of mathematical induction P(n) is true for all nonnegative integers n.
O There is nothing wrong with this proof.
O The proof is incorrect because you cannot add 1 to both sides of the equation in the inductive step.
O The proof is incorrect because the statement used in the inductive hypothesis is incorrect.
O The proof is incorrect because there is no basis step.

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