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1. Let us say that two integers are near one another provided the absolute value of their difference is 3 or smaller (i.e. the numbers are at most 3 apart). For example, 3 is near to 6, 10 is near 9, but 8 is not near 4. Let R stand for this is-near-to relation. Please do the following: a. Write down Ras a set of ordered pairs. Your answers should look like this: R = {(x, y): …} b. Prove or disprove: R is reflexive. c. Prove or disprove: R is irreflexive. d. Prove or disprove: R is symmetric. e. Prove or disprove: R is antisymmetric. f. Prove or disprove: R is transitive.

1. Let us say that two integers are near one another provided the absolute value of their difference is 3 or smaller (i.e. the numbers are at most 3 apart). For example, 3 is near to 6, 10 is near 9, but 8 is not near 4. Let R stand for this is-near-to relation. Please do the following: a. Write down Ras a set of ordered pairs. Your answers should look like this: R = {(x, y): …} b. Prove or disprove: R is reflexive. c. Prove or disprove: R is irreflexive. d. Prove or disprove: R is symmetric. e. Prove or disprove: R is antisymmetric. f. Prove or disprove: R is transitive.

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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1. Let us say that two integers are near one another provided the absolute value of their difference is 3 or smaller (i.e. the numbers are at most 3 apart). For example, 3 is near to 6, 10 is near 9, but 8 is not near 4. Let R stand for this is-near-to relation. Please do the following: a. Write down Ras a set of ordered pairs. Your answers should look like this: R = {(x, y): …} b. Prove or disprove: R is reflexive. c. Prove or disprove: R is irreflexive. d. Prove or disprove: R is symmetric. e. Prove or disprove: R is antisymmetric. f. Prove or disprove: R is transitive.
Transcribed Image Text:1. Let us say that two integers are near one another provided the absolute value of their difference is 3 or smaller (i.e. the numbers are at most 3 apart). For example, 3 is near to 6, 10 is near 9, but 8 is not near 4. Let R stand for this is-near-to relation. Please do the following: a. Write down Ras a set of ordered pairs. Your answers should look like this: R = {(x, y): …} b. Prove or disprove: R is reflexive. c. Prove or disprove: R is irreflexive. d. Prove or disprove: R is symmetric. e. Prove or disprove: R is antisymmetric. f. Prove or disprove: R is transitive.
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