1. Let (G, *) be a group, and let a, b, c e G. Which of the following does not always hold? A. a * b = a + c implies b = c B. (a + b)-1 = a-1 + b¬1 C. The linear equation y * a = b has a unique solution y in G. D. The identity element and inverse of each element are unique. 2. Let G = R\{-1}. Define + on G by a * b = a + ab + b. If 0 is the identity element in G, what is the inverse of a? А.- а B. a a C - a+1 D. -4 a+1 3. Let G = R\ {-1}. Define * on G by a * b = a + ab + b. Find the solution of the equation 3 * x * 2 = 23. А. 0 В. 1 C. ! D. -
1. Let (G, *) be a group, and let a, b, c e G. Which of the following does not always hold? A. a * b = a + c implies b = c B. (a + b)-1 = a-1 + b¬1 C. The linear equation y * a = b has a unique solution y in G. D. The identity element and inverse of each element are unique. 2. Let G = R\{-1}. Define + on G by a * b = a + ab + b. If 0 is the identity element in G, what is the inverse of a? А.- а B. a a C - a+1 D. -4 a+1 3. Let G = R\ {-1}. Define * on G by a * b = a + ab + b. Find the solution of the equation 3 * x * 2 = 23. А. 0 В. 1 C. ! D. -
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1.
Let (G, *) be a group, and let a, b, c e G. Which of the following does not always hold?
A. a * b = a + c implies b = c
B. (a + b)-1 = a-1 + b¬1
C. The linear equation y * a = b has a unique solution y in G.
D. The identity element and inverse of each element are unique.
2. Let G = R\{-1}. Define + on G by a * b = a + ab + b. If 0 is the identity element in
G, what is the inverse of a?
А.- а
B.
a
a
C -
a+1
D. -4
a+1
3. Let G = R\ {-1}. Define * on G by a * b = a + ab + b. Find the solution of the
equation 3 * x * 2 = 23.
А. 0
В. 1
C. !
D. -
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