Consider the relation R = {(n, m) e N × N ||n – m| < 1}. Then for example (1, 2) E Rsince |1 – 2| = 1 while (1,3) g R since |1 – 3|= 2.Prove or disprove each of the following statements:i. R is reflexive.ii. R is symmetric.iii. R is transitive.iv. R is countable.

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Answered: Consider the relation R {(n, m) e N x N…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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2. Let C = D = {-3, –2, –1, 1, 2, 3} and define a relation S from C to D as follows: For all (x, y) e C x D, 1 (x, y) E S means that 1 is an integer. y a. Is 2 S 2? Is –1S – 1? Is (2, 2) e S? Is (2, –-2) e S? b. Write S as a set of ordered pairs.
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Consider the relation R {(n, m) e N x N | |n – m| < 1}. Then for example (1,2) e R since |1 – 2| = 1 while (1, 3) g R since |1 – 3| = 2. %3D Prove or disprove each of the following statements: i. R is reflexive. ii. R is symmetric. iii. R is transitive. iv. R is countable.