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. R is a relation on the set of all people such that (a, b) E 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) E R 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 Zx Z such that ((a, b), (c,d)) = R if and only if a + b > c+d.
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. R is a relation on the set of all people such that (a, b) E 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) E R 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 Zx Z such that ((a, b), (c,d)) = R if and only if a + b > c+d.
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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Transcribed Image Text: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. R is a relation on the set of all people such that (a, b) E 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) E R 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 Zx Z such that ((a, b), (c,d)) = R if and only if a + b > c+d.
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