Prove the following statement by proving the contrapositive. Prove: If 3n +7 is an odd integer, then n is an even integer. Hint: When you prove the statement, these questions will guide you to prove that statement: • What is the contrapositive of the statement? • Is 3n even or odd? • What is an odd + odd? Is it even or odd? • What have you proved?

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 44E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
Question
Prove the following statement by proving the contrapositive.
Prove: If 3n +7 is an odd integer, then n is an even integer.
Hint: When you prove the statement, these questions will guide you to prove that statement:
• What is the contrapositive of the statement?
•
Is 3n even or odd?
• What is an odd + odd? Is it even or odd?
• What have you proved?
Transcribed Image Text:Prove the following statement by proving the contrapositive. Prove: If 3n +7 is an odd integer, then n is an even integer. Hint: When you prove the statement, these questions will guide you to prove that statement: • What is the contrapositive of the statement? • Is 3n even or odd? • What is an odd + odd? Is it even or odd? • What have you proved?
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