7. Let X be any set and let Y = "27X = {x : X → {0, 1}}, that is, Y is the set of all functionsfrom X to {0, 1}. Show that the map F: Y → P(X) defined below is a bijection:F :X+ {x E X |x(x) = 1} where xe 27X

To prove that F is a bijective mapping,we have to show that it is both one-to-one and onto.

Answered: Let X be any set and let Y = "2¬X = {x…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 2E: 2. Prove the following statements for arbitrary elements of an ordered integral domain . a....

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Let X be any set and let Y = "2¬X = {x : X → {0, 1}}, that is, Y is the set of all functions from X to {0, 1}. Show that the map F: Y → P(X) defined below is a bijection: F :X+ {x € X | x(x) = 1} where xe r27X