a.Given an integer a, then a² + 4a + 5 is odd if and only if a is even. b. There exists a positive real number x for which x2<√x. c. Suppose a€Z. Then a^2la if and only if a{-1,0,1}.
a.Given an integer a, then a² + 4a + 5 is odd if and only if a is even. b. There exists a positive real number x for which x2<√x. c. Suppose a€Z. Then a^2la if and only if a{-1,0,1}.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 39E
Related questions
Question
Please do all parts
Transcribed Image Text:Prove the following statement.
a.Given an integer a, then a² + 4a +5 is odd if and only if a is even.
b. There exists a positive real number x for which x2<√x.
c. Suppose aEZ. Then a^2la if and only if a{-1,0,1}.
d. Suppose a,beZ. If ab is odd, then a^2+b^2 is even.
e. If nEZ, then 4|n^2 or 41(n^2-1).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell