Kindly answer correctly. Show al he necessary steps 6. (Methods of proof) Consider the statementif n is an odd integer, then n? is an odd integer.(a) Give a direct proof of this statement.(b) Write down the contrapositive of the statement (don't need to prove it).(c) If you were attempting a proof by contradiction, what would be the hypotheses usedin your proof?

if n is an odd integer then we have to prove n^2 is an odd integer. a) let us consider n=2k+1 ,since…

fn is an odd integer, then n² is an odd integer. (a) Give a direet proof of this statement. (b) Write down the contrapositive of the statement (don't need to prove it). (e) If you were attempting a proof by contradiction, what would be the hypotheses used

fn is an odd integer, then n² is an odd integer. (a) Give a direet proof of this statement. (b) Write down the contrapositive of the statement (don't need to prove it). (e) If you were attempting a proof by contradiction, what would be the hypotheses used

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.5: Mathematical Induction

Problem 42E

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Question

Kindly answer correctly. Show al he necessary steps

6. (Methods of proof) Consider the statement
if n is an odd integer, then n? is an odd integer.
(a) Give a direct proof of this statement.
(b) Write down the contrapositive of the statement (don't need to prove it).
(c) If you were attempting a proof by contradiction, what would be the hypotheses used
in your proof?

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