1. Let X= (a, b, c) and Y {1, 2}.a) List all the subsets of X.b) List all the members of X XY.c) List all total functions from Y to X.2. Prove that the set of even integers is denumerable.3. Prove that the set of real numbers in the interval [0, 1] is uncountable. Hint: Use thediagonalization argument on the decimal expansion of real numbers.

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1. Let X= (a, b, c) and Y {1, 2}. a) List all the subsets of X. b) List all the members of X XY. c) List all total functions from Y to X.

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

1. Let X= (a, b, c) and Y {1, 2}.
a) List all the subsets of X.
b) List all the members of X XY.
c) List all total functions from Y to X.
2. Prove that the set of even integers is denumerable.
3. Prove that the set of real numbers in the interval [0, 1] is uncountable. Hint: Use the
diagonalization argument on the decimal expansion of real numbers.

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