13. Imagine finite sets X and Y and denote by {f: X Y} the set of...
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13. Imagine finite sets X and Y and denote by {f: X→ Y} the set of all functions from X to Y. (a) Take X = {a,b} and Y = {1,2,3} and write down all elements of the set {f: X→ Y}. (b) Assume that Y = {0, 1}. Give a bijection between {f: X→ Y} and 2X. Hint: indicator functions. (c) Prove that for any finite X, Y the following holds: I #{f: X →Y} = (#Y)#X 13. Imagine finite sets X and Y and denote by {f: X→ Y} the set of all functions from X to Y. (a) Take X = {a,b} and Y = {1,2,3} and write down all elements of the set {f: X→ Y}. (b) Assume that Y = {0, 1}. Give a bijection between {f: X→ Y} and 2X. Hint: indicator functions. (c) Prove that for any finite X, Y the following holds: I #{f: X →Y} = (#Y)#X
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Answer rating: 100% (QA)
a There are six functions from X to Y f1a 1 f1b 2 f2a 1 f2b 3 f3a 2 f3b 1 f4a 2 f4b 3 f5a ... View the full answer
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Posted Date:
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