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4. Consider the following relations R on the integers Z. For each of these relations, say whether the following statements are true or false: (i) R is reflexive; (ii) R is symmetric; (iii) R is a function; (iv) R is irreflexive. a. R= {(n, m) E Z x Z[ m = {(n,m) E Z x Z| (n is even A m is odd) V (n is odd A m is even)}. = {(n,m) E Z x Z| m = 100}. b. R= - -n}.

4. Consider the following relations R on the integers Z. For each of these relations, say whether the following statements are true or false: (i) R is reflexive; (ii) R is symmetric; (iii) R is a function; (iv) R is irreflexive. a. R= {(n, m) E Z x Z[ m = {(n,m) E Z x Z| (n is even A m is odd) V (n is odd A m is even)}. = {(n,m) E Z x Z| m = 100}. b. R= - -n}.

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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4. Consider the following relations R on the integers Z. For each of these relations, say whether the following statements are true or false: (i) R is reflexive; (ii) R is symmetric; (iii) R is a function; (iv) R is irreflexive. a. R= {(n, m) EZ x Z| m = 100}. b. R= {(n,m) EZ x Z| (n is even A m is odd) V (n is odd A m is even)}. %3D c. R= {(n,m) EZ x Z| m = – = -n}.
Transcribed Image Text:4. Consider the following relations R on the integers Z. For each of these relations, say whether the following statements are true or false: (i) R is reflexive; (ii) R is symmetric; (iii) R is a function; (iv) R is irreflexive. a. R= {(n, m) EZ x Z| m = 100}. b. R= {(n,m) EZ x Z| (n is even A m is odd) V (n is odd A m is even)}. %3D c. R= {(n,m) EZ x Z| m = – = -n}.
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