] In the following claim and proof by Principle of Mathematical Induction decide whether the basis step, inductive assumption and inductive proof is correct, partially correct or wrong. "5 divides 23n – 3" for all natural numbers n". Basis step: For n = 0, 23n – 3" = 1-1 = 0 and 5 divides 0. O correct. O partially correct. O wrong Inductive Assumption: Assume that 5 divides (23K -34). So (23K – 3k = 5m) for Some integer m. O correct. O partially correct. O wrong. Inductive Proof: We need to prove that 5 divides (23k+1-3*+1). Note that (23k +1–3*+1=2(23*)-3(3*)= (2 – 3)(2³K – 3*). So hypothesis is satisfied for n-k+1. By PMI, "5 divides (23n – 3") for all natural numbers n". O correct. O partially correct. O wrong.

] In the following claim and proof by Principle of Mathematical Induction decide whether the basis step, inductive assumption and inductive proof is correct, partially correct or wrong. "5 divides 23n – 3" for all natural numbers n". Basis step: For n = 0, 23n – 3" = 1-1 = 0 and 5 divides 0. O correct. O partially correct. O wrong Inductive Assumption: Assume that 5 divides (23K -34). So (23K – 3k = 5m) for Some integer m. O correct. O partially correct. O wrong. Inductive Proof: We need to prove that 5 divides (23k+1-3+1). Note that (23k +1–3+1=2(23)-3(3)= (2 – 3)(2³K – 3*). So hypothesis is satisfied for n-k+1. By PMI, "5 divides (23n – 3") for all natural numbers n". O correct. O partially correct. O wrong.

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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Question

|In the following claim and proof by Principle of
Mathematical Induction decide whether the basis step, inductive
assumption and inductive proof is correct, partially correct or
wrong.
"5 divides 23n - 3" for all natural numbers n".
Basis
step: For n = 0, 23n – 3" = 1-1= 0 and 5 divides 0.
O correct.
O partially correct.
Owrong
Inductive Assumption: Assume that 5 divides (23K - 34). So
(23K – 3K = 5m) foF Some integer m.
O partially correct.
) O wrong
O correct.
Inductive Proof: We need to prove that 5 divides
(23k +1-3k+1). Note that
(23k +1-3k+1=2(23)-3(3*)= (2– 3)(23* –3*). So
hypothesis is satisfied for n=k+1. By PMI, "5 divides (2n - 3")
for all natural numbers n".
O correct.
O partially correct.
O wrong.

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