Required informationNOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.For each of these relations on the set (1, 2, 3, 4), decide whether it is reflexive, symmetric, antisymmetric, or transitive.(1. 1). (1, 2). (2. 1). (2, 2). (3, 3). (4. 4) (Check all that apply.)Check All That Applytransitivesymmetricantisymmetricreflexive

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Answered: 1. 2). (2. 1). (2. 2). (3. 3). (4, 4)…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...

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Similar questions

In each of the following parts, a relation is defined on the set of all human beings. Determine whether the relation is reflective, symmetric, or transitive. Justify your answers. xRy if and only if x lives within 400 miles of y. xRy if and only if x is the father of y. xRy if and only if x is a first cousin of y. xRy if and only if x and y were born in the same year. xRy if and only if x and y have the same mother. xRy if and only if x and y have the same hair colour.
Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.
Find mappings f,g and h of a set A into itself such that fg=hg and fh. Find mappings f,g and h of a set A into itself such that fg=fh and gh.
Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.
True or False Label each of the following statements as either true or false. Two sets are equal if and only if they contain exactly the same elements.
13. Consider the set of all nonempty subsets of . Determine whether the given relation on is reflexive, symmetric or transitive. Justify your answers. a. if and only if is subset of . b. if and only if is a proper subset of . c. if and only if and have the same number of elements.
True or False Label each of the following statements as either true or false. The set ZZ+ is closed with respect to subtraction.

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1. 2). (2. 1). (2. 2). (3. 3). (4, 4) (Check all that apply) Check All That Apply