Let X be a set and XX the set of all functions from X into X. Show that function composition on X is associative on XX. Then prove or disprove if the composition of injective functions is injective.
Let X be a set and XX the set of all functions from X into X. Show that function composition on X is associative on XX. Then prove or disprove if the composition of injective functions is injective.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.3: Properties Of Composite Mappings (optional)
Problem 8E: Suppose f,g and h are all mappings of a set A into itself. a. Prove that if g is onto and fg=hg,...
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Let X be a set and XX the set of all functions from X into X. Show that function composition on X is associative on XX. Then prove or disprove if the composition of injective functions is injective.
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