Prove the following statements: 1. Suppose and y are even integers, then x + y is even. 2. Suppose x is an even integer and y is an odd integer, then x + y is odd. 3. If x is an integer and y is odd, then xy has the same parity as x. 4. If x is an integer, then ² has the same parity as x. 5. If x is an integer, then x² + 3x + 3 is odd.
Prove the following statements: 1. Suppose and y are even integers, then x + y is even. 2. Suppose x is an even integer and y is an odd integer, then x + y is odd. 3. If x is an integer and y is odd, then xy has the same parity as x. 4. If x is an integer, then ² has the same parity as x. 5. If x is an integer, then x² + 3x + 3 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:Prove the following statements:
1. Suppose and y are even integers, then x + y is even.
2. Suppose x is an even integer and y is an odd integer, then
x + y is odd.
3. If x is an integer and y is odd, then xy has the same parity
as x.
4. If x is an integer, then ² has the same parity as x.
5. If x is an integer, then x² + 3x + 3 is odd.
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