S De a set of n numbers, and let k De a natura less than equal n. Let X Be the set of all subsets of S of size k, and let Y be the set of all ordered k-tuples (s1, S2, such that s, < s, < ·..< S. That is, ... X = {{s1,$2,...,Sk} | $¿ € S and all s;'s are distinct}, and Y = {($1,82,..., Sk) | $¿ E S and s1 < s2 < ..< sk}. %3D (a) Define a one-to-one correspondence f : X → Y. Explain why f is one-to-one and onto.

S De a set of n numbers, and let k De a natura less than equal n. Let X Be the set of all subsets of S of size k, and let Y be the set of all ordered k-tuples (s1, S2, such that s, < s, < ·..< S. That is, ... X = {{s1,$2,...,Sk} | $¿ € S and all s;'s are distinct}, and Y = {($1,82,..., Sk) | $¿ E S and s1 < s2 < ..< sk}. %3D (a) Define a one-to-one correspondence f : X → Y. Explain why f is one-to-one and onto.

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

Section: Chapter Questions

Problem 1PE

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Question

Define a one-to-one correspondence f : X → Y. Explain why f is one-to-one and
onto.

Let S be a set of n numbers, and let k be a natural number less than or equal to n. Let X be
the set of all subsets of S of size k, and let Y be the set of all ordered k-tuples (s1, 82,
such that s, < S2
•...
< $p. That is,
X = {{s1,$2,...,Sk} | S¡ E S and all s;'s are distinct}, and
Y = {($1,82,..., Sk) | S; ES and s1 < s2 < ·…< sSk}.
(a) Define a one-to-one correspondence f : X → Y. Explain why f is one-to-one and
onto.

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