For each of the functions below, determine and prove whether or not it is injective, surjective, and bijective. 1. ƒ : {0, 1}³ → {0, 1}¹ is given by adding a copy of the first bit to the end of the binary string. In other words f(xyz) = xyzx. 2. Let S = {1, 2, 3} and consider g : P(S) → {0, 1, 2, 3} given by g(A) = |A|, where recall that for any set A, |A| denotes its cardinality.

For each of the functions below, determine and prove whether or not it is injective, surjective, and bijective. 1. ƒ : {0, 1}³ → {0, 1}¹ is given by adding a copy of the first bit to the end of the binary string. In other words f(xyz) = xyzx. 2. Let S = {1, 2, 3} and consider g : P(S) → {0, 1, 2, 3} given by g(A) = |A|, where recall that for any set A, |A| denotes its cardinality.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

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