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Suppose A, B C U, (A, +, –( ),0) e Grp (A), and (B,*,-( ),0) e Grp(B). If we define (u – v) to be (u + (-v)) for both groups, prove that for all ø e Fnc(A, B), that $ is a group homomorphism from A to B if

Suppose A, B C U, (A, +, –( ),0) e Grp (A), and (B,*,-( ),0) e Grp(B). If we define (u – v) to be (u + (-v)) for both groups, prove that for all ø e Fnc(A, B), that $ is a group homomorphism from A to B if

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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Suppose ?, ? ⊆ ?,⟨?, +, −( ), 0⟩ ∈ ??? (?), and ⟨?,∗, −( ), 0́⟩ ∈ ???(?).
If we define (? − ?) to be (? + (−?)) for both groups, prove that for all ? ∈ ???(?, ?), that
? is a group homomorphism from A to B if
?(? − ?) = (?(?) − ?(?)).

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Suppose A, B C U, (A, +, –( ),0) E Grp (A), and (B,*,-),ó) e Grp(B). If we define (u – v) to be (u + (-v)) for both groups, prove that for all ø e Fnc(A, B), that p is a group homomorphism from A to B if Ф(а — b) %3D (ф(а) - ФБ)).
Transcribed Image Text:Suppose A, B C U, (A, +, –( ),0) E Grp (A), and (B,*,-),ó) e Grp(B). If we define (u – v) to be (u + (-v)) for both groups, prove that for all ø e Fnc(A, B), that p is a group homomorphism from A to B if Ф(а — b) %3D (ф(а) - ФБ)).
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