01. Prove the following conjecture: The sum of any two consecutive integers can be written in the form 4n +1 where n is some integer. 02. Prove the following conjecture: If n is even, then 7n + 4 is even. 03. Prove by contradiction: Let a , b be the side lengths of a right triangle. Let c be the length of the hypotenuse of the right triangle. Prove c > a +b 04. Prove by contradiction: For all integers n , If n ^ 3 is odd then n is odd.
01. Prove the following conjecture: The sum of any two consecutive integers can be written in the form 4n +1 where n is some integer. 02. Prove the following conjecture: If n is even, then 7n + 4 is even. 03. Prove by contradiction: Let a , b be the side lengths of a right triangle. Let c be the length of the hypotenuse of the right triangle. Prove c > a +b 04. Prove by contradiction: For all integers n , If n ^ 3 is odd then n is odd.
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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Transcribed Image Text:01. Prove the following conjecture:
The sum of any two consecutive integers can be written in the form 4n +1 where n is some integer.
02. Prove the following conjecture: If n is even, then 7n + 4 is even.
03. Prove by contradiction:
Let a , b be the side lengths of a right triangle.
Let c be the length of the hypotenuse of the right triangle.
Prove c > a +b
04. Prove by contradiction:
For all integers n , If n ^ 3 is odd then n is odd.
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