Given the input set A = {1, 2, 3, 4, 5} and output set B = {1,  2, 3, 4}, is it possible to find a hash function H from A to B that has no hash collision, i.e.,   LaTeX: \forall ∀ a1, a2 LaTeX: \in ∈A, H(a1) LaTeX: \ne ≠H(a2)   If yes, please give the function. Otherwise, please explain. (Hint: pigeonhole principle)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Given the input set A = {1, 2, 3, 4, 5} and output set B = {1,  2, 3, 4}, is it possible to find a hash function H from A to B that has no hash collision, i.e.,

 

LaTeX: \forall ∀ a1, a2 LaTeX: \in ∈A, H(a1) LaTeX: \ne ≠H(a2)

 

If yes, please give the function. Otherwise, please explain. (Hint: pigeonhole principle)

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