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4. Show that the function f : X → Y defined by f(X) = X U {a} vX €x is a bijection.

4. Show that the function f : X → Y defined by f(X) = X U {a} vX €x is a bijection.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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4. Show that the function f : X → Y defined by f(X) = XU {a} VX € X is a bijection.
Transcribed Image Text:4. Show that the function f : X → Y defined by f(X) = XU {a} VX € X is a bijection.
Let k e Zt. Let A be a set such that |A| = k + 1, and let a € A (i.e., a is a fixed but unspecified element of A). Define X:= {X | X C A and a ¢ X} Y := {Y | Y C A and a E Y}
Transcribed Image Text:Let k e Zt. Let A be a set such that |A| = k + 1, and let a € A (i.e., a is a fixed but unspecified element of A). Define X:= {X | X C A and a ¢ X} Y := {Y | Y C A and a E Y}
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