Detailed
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 80E
Related questions
Question
Detailed prove for number 4
![ch.iastate.edu/class/BookOfProof.pdf
Exercises for Chapter 7
Prove the following statements. These exercises are cumulative, covering all
techniques addressed in Chapters 4-7.
1. Suppose x e Z. Then x is even if and only if 3x+5 is odd.
2. Suppose xe 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 even.
4. 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 e R. Then x³ + x²y = y² + xy if and only if y=x² or y=-x.
Then (x + y)² = x² + y² if and only if x = 0 or y = 0.
7. Suppose x,y e R.
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).
F4
11. Suppose a, b e Z. Prove that (a-3)62 is even if and only if a is odd or b is even.
12. There exist a positive real number x for which x² <√√x.
13. Suppose a, b e Z. If a + b is odd, then a² + b² is odd.
14. Suppose a € Z. Then a² la if and only if a € (-1,0,1}.
15. Suppose a, b € Z. Prove that a + b is even if and only if a and b have the same
parity.
16. Suppose a, b e Z. If ab is odd, then a² + b² is even.
17. There is a prime number between 90 and 100.
18. There is a set X for which NE X and N≤X.
19. If ne N, then 20 +2¹+22 +23+24+...+2 = 2n+1 -1.
20. There exists an neN for which 11 (2-1).
!!
A
-O
F6
CD A
-..
F7
HI
ų
F8
(T)
F9
prt sc
F10
home
8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3cd21fb3-e059-4805-be9c-60b9d1b235c0%2F9240efff-34cf-4562-8654-a822c4e54246%2Fc5p6yg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:ch.iastate.edu/class/BookOfProof.pdf
Exercises for Chapter 7
Prove the following statements. These exercises are cumulative, covering all
techniques addressed in Chapters 4-7.
1. Suppose x e Z. Then x is even if and only if 3x+5 is odd.
2. Suppose xe 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 even.
4. 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 e R. Then x³ + x²y = y² + xy if and only if y=x² or y=-x.
Then (x + y)² = x² + y² if and only if x = 0 or y = 0.
7. Suppose x,y e R.
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).
F4
11. Suppose a, b e Z. Prove that (a-3)62 is even if and only if a is odd or b is even.
12. There exist a positive real number x for which x² <√√x.
13. Suppose a, b e Z. If a + b is odd, then a² + b² is odd.
14. Suppose a € Z. Then a² la if and only if a € (-1,0,1}.
15. Suppose a, b € Z. Prove that a + b is even if and only if a and b have the same
parity.
16. Suppose a, b e Z. If ab is odd, then a² + b² is even.
17. There is a prime number between 90 and 100.
18. There is a set X for which NE X and N≤X.
19. If ne N, then 20 +2¹+22 +23+24+...+2 = 2n+1 -1.
20. There exists an neN for which 11 (2-1).
!!
A
-O
F6
CD A
-..
F7
HI
ų
F8
(T)
F9
prt sc
F10
home
8
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