For each of the following relations, determine whether the relation is:• Transitive.• A partial order.• A strict order.• An equivalence relation.Reflexive.Anti-reflexive.Symmetric.• Anti-symmetric.Justify all your answers.a. Ris a relation on the set of all people such that (a, b) e R if and only if a and b have acommon grandparent.b. Ris a relation on Z such that (x, y) E R if and only if |x – y| < 2.c. Ris a relation on Z* such that (x, y) E R if and only if x is divisible by y. Hint: An integerx is divisible by an integer y with y # 0 if and only if there exists an integer k such thatx = yk.d. Ris a relation on Z* such that (x, y) E R if and only if there is a positive integer n suchthat x" = y.e. Ris a relation on Z x Z such that ((a, b), (c, d)) E R if and only if a < c and b < d.

Reflexive: Yes(x, x) belongs to R for all x in the set Anti-reflexive: NoIt is reflexive Symmetric:…

Reflexive. Transitive. • A partial order. • A strict order. • An equivalence relation. Anti-reflexive. Symmetric. Anti-symmetric. Justify all your answers. a. Ris a relation on the set of all people such that (a, b) e R if and only if a and b have a common grandparent.

Reflexive. Transitive. • A partial order. • A strict order. • An equivalence relation. Anti-reflexive. Symmetric. Anti-symmetric. Justify all your answers. a. Ris a relation on the set of all people such that (a, b) e R if and only if a and b have a common grandparent.

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

For each of the following relations, determine whether the relation is:
• Transitive.
• A partial order.
• A strict order.
• An equivalence relation.
Reflexive.
Anti-reflexive.
Symmetric.
• Anti-symmetric.
Justify all your answers.
a. Ris a relation on the set of all people such that (a, b) e R if and only if a and b have a
common grandparent.
b. Ris a relation on Z such that (x, y) E R if and only if |x – y| < 2.
c. Ris a relation on Z* such that (x, y) E R if and only if x is divisible by y. Hint: An integer
x is divisible by an integer y with y # 0 if and only if there exists an integer k such that
x = yk.
d. Ris a relation on Z* such that (x, y) E R if and only if there is a positive integer n such
that x" = y.
e. Ris a relation on Z x Z such that ((a, b), (c, d)) E R if and only if a < c and b < d.

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