Prove the following statementsANSWER #1 ONLY 1. Suppose x € Z. Then x is even if and only if 3x +5 is odd.2. Suppose x € Z. Then x is odd if and only if 3x + 6 is odd.3. Given an integer a, then a³ + a² +a is even if and only if a is ever4. Given an integer a, then a² + 4a +5 is odd if and only if a is even.5. An integer a is odd if and only if a³ is odd.6. Suppose x, y € R. Then x³+x²y = y² + xy if and only if y=x² or y=-x.7. Suppose x, y € R. Then (x + y)² = x² + y² if and only if x = 0 or y = 0.8. Suppose a,b € Z. Prove that a = b (mod 10) if and only if a = b (mod 2) and a = b(mod 5).9. Suppose a € Z. Prove that 14|a if and only if 7 | a and 2 | a.10. If a € Z, then a³ = a (mod 3).

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Answered: 1. Suppose x € Z. Then x is even if and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Please I want a detailed prove for 6,7,8
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1. Suppose x € Z. Then x is even if and only if 3x + 5 is odd. 2. Suppose x € Z. Then x is odd if and only if 3x + 6 is odd.