Recall the defintion of the power set of an arbitrary set, A: We say the set of all subsets of A, denoted 24,is the power set of A.Let A = {a, b, c} be a set of three elements. Consider the set functionf : 24 → Zdefined by f(B) = |B| that is, the image of a subset of A under ƒ is the number of its elements.Draw a diagram that illustrates this function that includes both its domain and its image. Use this diagramin conjunction with the definition to illustrate why f is not an injection i.e. is not 1-1.

Given function is, So, the required diagram is,

Recall the defintion of the power set of an arbitrary set, A: We say the set of all subsets of A, denoted 2ª, is the power set of A. Let A = {a, b, c} be a set of three elements. Consider the set function f: 24 →Z defined by f(B) = |B| that is, the image of a subset of A under f is the number of its elements. Draw a diagram that illustrates this function that includes both its domain and its image. Use this diagram in conjunction with the definition to illustrate why ƒ is not an injection i.e. is not 1-1.

Recall the defintion of the power set of an arbitrary set, A: We say the set of all subsets of A, denoted 2ª, is the power set of A. Let A = {a, b, c} be a set of three elements. Consider the set function f: 24 →Z defined by f(B) = |B| that is, the image of a subset of A under f is the number of its elements. Draw a diagram that illustrates this function that includes both its domain and its image. Use this diagram in conjunction with the definition to illustrate why ƒ is not an injection i.e. is not 1-1.

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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Recall the defintion of the power set of an arbitrary set, A: We say the set of all subsets of A, denoted 24,
is the power set of A.
Let A = {a, b, c} be a set of three elements. Consider the set function
f : 24 → Z
defined by f(B) = |B| that is, the image of a subset of A under ƒ is the number of its elements.
Draw a diagram that illustrates this function that includes both its domain and its image. Use this diagram
in conjunction with the definition to illustrate why f is not an injection i.e. is not 1-1.

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