"Consider the following binary relations on the naturals (non-negative integers). Which onesare reflexive? Symmetric? Anti-symmetric? Transitive? Partial orders? Justify your claims.(a) A(x, y), defined to be true if and only if y is even.(b) B(x, y), defined to be true if and only if x < y.(c) C(x, y), defined to be true if and only if x + 2 ≥ y.(d) D(x, y), defined to be true if and only if x = y.(e) E(x, y), defined to be true if and only if the English name of x comes no later than thename of y in alphabetical order. (So, for example, E(8, 81) is true because eight comesbefore eighty-one, and E(8, 8) is true because eight comes no later than eight
"Consider the following binary relations on the naturals (non-negative integers). Which onesare reflexive? Symmetric? Anti-symmetric? Transitive? Partial orders? Justify your claims.(a) A(x, y), defined to be true if and only if y is even.(b) B(x, y), defined to be true if and only if x < y.(c) C(x, y), defined to be true if and only if x + 2 ≥ y.(d) D(x, y), defined to be true if and only if x = y.(e) E(x, y), defined to be true if and only if the English name of x comes no later than thename of y in alphabetical order. (So, for example, E(8, 81) is true because eight comesbefore eighty-one, and E(8, 8) is true because eight comes no later than eight
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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"Consider the following binary relations on the naturals (non-negative integers). Which onesare reflexive? Symmetric? Anti-symmetric? Transitive? Partial orders? Justify your claims.(a) A(x, y), defined to be true if and only if y is even.(b) B(x, y), defined to be true if and only if x < y.(c) C(x, y), defined to be true if and only if x + 2 ≥ y.(d) D(x, y), defined to be true if and only if x = y.(e) E(x, y), defined to be true if and only if the English name of x comes no later than thename of y in alphabetical order. (So, for example, E(8, 81) is true because eight comesbefore eighty-one, and E(8, 8) is true because eight comes no later than eight
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