1. Let A be a non-empty set and (G, .) be a group. Let F be the set of all functions from A to G. Define an operation * on F as follows: For f,g E F, let f * g : A → G as (f * g)(x) = f(x). g(x) V x E A.
1. Let A be a non-empty set and (G, .) be a group. Let F be the set of all functions from A to G. Define an operation * on F as follows: For f,g E F, let f * g : A → G as (f * g)(x) = f(x). g(x) V x E A.
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 A be a non-empty set and (G,.) be a group. Let F be the set of all functions from A to G. Define
an operation * on F as follows:
For f,g € F, let f * g : A → G as (f * g)(x) = f(x). g(x) V x € A.
Prove that (F,* ) is a group.
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