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 37E
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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).
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