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QUESTION 10 Let A = R/{0}, the real numbers without 0 and S={f ,g,h,k} where these are functions 1 from A to A def ined by f (x) =1, g (x) =-, h (x) = -x, and k(x) =--. Write the operations table (Cayley Table) for S under compositon and explain why this is a group.

QUESTION 10 Let A = R/{0}, the real numbers without 0 and S={f ,g,h,k} where these are functions 1 from A to A def ined by f (x) =1, g (x) =-, h (x) = -x, and k(x) =--. Write the operations table (Cayley Table) for S under compositon and explain why this is a group.

Advanced Engineering Mathematics
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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Abstract Algebra 1
QUESTION 10 Let A = R/{0}, the real numbers without 0 and S={f,g,h,k} where these are functions 1 1 from A to A def ined by f (x) =1, g (x) =-, h (x) = -x, and k(x) =--. Write the operations table (Cayley Table) for S under compositon and explain why this is a group.
Transcribed Image Text:QUESTION 10 Let A = R/{0}, the real numbers without 0 and S={f,g,h,k} where these are functions 1 1 from A to A def ined by f (x) =1, g (x) =-, h (x) = -x, and k(x) =--. Write the operations table (Cayley Table) for S under compositon and explain why this is a group.
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