I have the following question: "Prove that if n is an odd integer, then 7n − 5 is even by (a) a proof by contrapositive and (b) a proof by contradiction." I have the following solution but I'm not quite sure if its right, I know there are some writing style mistakes but is the general way of solving these proofs right?: For (a), If 7n-5 is odd then 'n' is even. 7n-5=2k+1 we need to show that 'n'
I have the following question: "Prove that if n is an odd integer, then 7n − 5 is even by (a) a proof by contrapositive and (b) a proof by contradiction." I have the following solution but I'm not quite sure if its right, I know there are some writing style mistakes but is the general way of solving these proofs right?: For (a), If 7n-5 is odd then 'n' is even. 7n-5=2k+1 we need to show that 'n'
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I have the following question:
"Prove that if n is an odd integer, then 7n − 5 is even by
(a) a proof by contrapositive and (b) a proof by contradiction."
I have the following solution but I'm not quite sure if its right, I know there are some writing style mistakes but is the general way of solving these proofs right?:
For (a), If 7n-5 is odd then 'n' is even. 7n-5=2k+1 we need to show that 'n' is even,
n= (7n-5) + (-6n+5) = 2k+1-6n+5 = 2k-6n+6 = 2(k-3n+3).
Since (k-3n+3) is an integer 'n' is even.
For (b), If 'n' is an even integer, then 7n-5 is odd.
If n = 2x, then 7(2x)-5=2(7x)-5. Since (7x) is an integer 7n-5 is odd.
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