2. Is * commutative? If it is commutative, show it. Otherwise, give a counterexample.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 87E
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Can you answer letter C, no. 2?
A. Prove that (n - a)? = (mod n)
B. Is the function f: R →R where f(x) = x? injective? Surjective? Support your answer.
С.
Let the binary operation * be defined on S = {a, b, c, d, e} by means of a given table.
a
b
d
е
a
a
b
d
e
b
a
e
C
C
a
b
b
a
d
b
e
b
e
d.
e
b
a d c
1. Compute b * d, c * c and [(a * c) * c], from the table.
2. Is * commutative? If it is commutative, show it. Otherwise, give a counterexample.
3. Is * associative? If it is associative, show it. Otherwise, give a counterexample.
Transcribed Image Text:A. Prove that (n - a)? = (mod n) B. Is the function f: R →R where f(x) = x? injective? Surjective? Support your answer. С. Let the binary operation * be defined on S = {a, b, c, d, e} by means of a given table. a b d е a a b d e b a e C C a b b a d b e b e d. e b a d c 1. Compute b * d, c * c and [(a * c) * c], from the table. 2. Is * commutative? If it is commutative, show it. Otherwise, give a counterexample. 3. Is * associative? If it is associative, show it. Otherwise, give a counterexample.
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