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. Reflexive. Anti-reflexive. For each of the following relations, determine whether the relation is: Transitive. Symmetric. • Anti-symmetric. • A partial order. A strict order. . An equivalence relation. Justify all your answers. a. R is a relation on the set of all people such that (a,b) = R if and only if a has the same first name or the same last name as b. b. R is a relation on a power set such that (A,B) ER if and only if |A| = |B| (i.e., the cardinality of A is equal to the cardinality of B). c. R is a relation on Z such that (a, b) E R if and only if |a| = |b| +1.

. Reflexive. Anti-reflexive. For each of the following relations, determine whether the relation is: Transitive. Symmetric. • Anti-symmetric. • A partial order. A strict order. . An equivalence relation. Justify all your answers. a. R is a relation on the set of all people such that (a,b) = R if and only if a has the same first name or the same last name as b. b. R is a relation on a power set such that (A,B) ER if and only if |A| = |B| (i.e., the cardinality of A is equal to the cardinality of B). c. R is a relation on Z such that (a, b) E R if and only if |a| = |b| +1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For each of the following relations, determine whether the relation is: Transitive. • A partial order. Reflexive. . Anti-reflexive. Symmetric. • Anti-symmetric. A strict order. . An equivalence relation. Justify all your answers. a. R is a relation on the set of all people such that (a,b) = R if and only if a has the same first name or the same last name as b. b. R is a relation on a power set such that (A,B) ER if and only if |A| = |B| (i.e., the cardinality of A is equal to the cardinality of B). c. R is a relation on Z such that (a,b) = R if and only if |a| = |b| +1. d. R is a relation on Z such that (a, b) = R if and only if a+b>1. e. R is a relation on ZxZ such that ((a, b), (c, d)) = R if and only if a+b>c+d.
Transcribed Image Text:For each of the following relations, determine whether the relation is: Transitive. • A partial order. Reflexive. . Anti-reflexive. Symmetric. • Anti-symmetric. A strict order. . An equivalence relation. Justify all your answers. a. R is a relation on the set of all people such that (a,b) = R if and only if a has the same first name or the same last name as b. b. R is a relation on a power set such that (A,B) ER if and only if |A| = |B| (i.e., the cardinality of A is equal to the cardinality of B). c. R is a relation on Z such that (a,b) = R if and only if |a| = |b| +1. d. R is a relation on Z such that (a, b) = R if and only if a+b>1. e. R is a relation on ZxZ such that ((a, b), (c, d)) = R if and only if a+b>c+d.
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