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15. If n €Z, then n² +3n +4 is even. (Try cases.) 16. If two integers have the same parity, then their sum is even. (Try cases.) 17. If two integers have opposite parity, then their product is even.

15. If n €Z, then n² +3n +4 is even. (Try cases.) 16. If two integers have the same parity, then their sum is even. (Try cases.) 17. If two integers have opposite parity, then their product is even.

Advanced Engineering Mathematics
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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### Mathematical Statements and Proofs 15. **Statement**: If \( n \in \mathbb{Z} \), then \( n^2 + 3n + 4 \) is even. **Suggestion**: Try cases. 16. **Statement**: If two integers have the same parity, then their sum is even. **Suggestion**: Try cases. 17. **Statement**: If two integers have opposite parity, then their product is even. These statements explore properties of integers with respect to parity (evenness or oddness). Testing through various cases aids in understanding and proving these mathematical assertions.
Transcribed Image Text:### Mathematical Statements and Proofs 15. **Statement**: If \( n \in \mathbb{Z} \), then \( n^2 + 3n + 4 \) is even. **Suggestion**: Try cases. 16. **Statement**: If two integers have the same parity, then their sum is even. **Suggestion**: Try cases. 17. **Statement**: If two integers have opposite parity, then their product is even. These statements explore properties of integers with respect to parity (evenness or oddness). Testing through various cases aids in understanding and proving these mathematical assertions.
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