Explanation Given information: R and S are antisymmetric . Concept used: Let R be a relation on a set A . Then R is said to be anti-symmetric relation if and only if x R y and y R x implies x = y for every x , y ∈ A . Calculation: A relation R on a set A is such that it is reflexive, symmetric, transitive, and antisymmetric. The objective is to find the kind of relation R is. Reflexive: Let R be a reltion on a set A . Then R is reflexive if, and only if, for all x ∈ A , x R x or ( x , x ) ∈ R . Symmetric: Let R be a relation on a set A . Then R is symmetric if, and only if, for all x , y ∈ A , if x R y ( or ( x , y ) ∈ R ) then y R x ( or ( y , x ) ∈ R ) . Transitive: let R be a relation on a set A .Then R is transitive if, and only if, for all x , y , z ∈ A , if x R y and y R z , then x R z . That is, if ( x , y ) ∈ R and ( y , z ) ∈ R then ( x , z ) ∈ R . Antisymmetric: let R be a relation on a set A . Then R is antisymmetric if, and only if, for all x , y ∈ A , if x R y and y R x , then x = y

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ISBN: 9780357540244

Author: EPP

Publisher: CENGAGE L

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Chapter 8.5, Problem 15ES

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The conclusion about R if it is reflexive, symmetric, transitive, and antisymmetric.

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Chapter 8.5, Problem 14ES

Chapter 8.5, Problem 16ES

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Chapter 8 Solutions

WEBASSIGN F/EPPS DISCRETE MATHEMATICS

Ch. 8.1 - If R is a relation from A to B, xA , and yB , the...Ch. 8.1 - Prob. 2TY Ch. 8.1 - Prob. 3TY Ch. 8.1 - Prob. 4TY Ch. 8.1 - If R is a relation on a set A, the directed graph...Ch. 8.1 - As in Example 8.1.2, the congruence modulo 2...Ch. 8.1 - Prove that for all integers m and n,m-n is even...Ch. 8.1 - The congruence modulo 3 relation, T, is defined...Ch. 8.1 - Define a relation P on Z as follows: For every...Ch. 8.1 - Prob. 5ES

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The conclusion about R if it is reflexive, symmetric, transitive, and antisymmetric.

Solution Summary: The author explains how the relation R is reflexive, symmetric, transitive and antisymmetric.

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To find: The conclusion about R if it is reflexive, symmetric, transitive, and antisymmetric.

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Chapter 8 Solutions

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The conclusion about R if it is reflexive, symmetric, transitive, and antisymmetric.