Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

Use quantifiers to express what it means for a relation to be asymmetric.

$\forall a \forall b ((a, b) \in R \to (b, a) \notin R)$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

An asymmetric relation.

Step 2: Concept used of relation

A relation $R$ on a set $A$ is called reflexive if $(a, a) \in R$ for every element $a \in A$ .

A relation $R$ on a set $A$ is called symmetric if $(b, a) \in R$ whenever $(a, b) \in R$ , for all $a, b \in A$

A relation $R$ on a set $A$ such that for all $a, b \in A$ , if $(a, b) \in R$ and $(b, a) \in R$ then $a = b$ is called anti symmetric.

A relation $R$ on a set $A$ is called transitive if whenever $(a, b) \in R$ and $(b, c) \in R$ then $(a, c) \in R$ for all $a, b, c \in A$

Step 3: Solve for relation

We know that $R$ is called asymmetric if $(a, b) \in R$ implies that $(b, a) \notin R$ .

Using quantifiers we see that a relation $R$ on the set $A$ is asymmetric if we have $\forall a \forall b ((a, b) \in R \to (b, a) \notin R)$ where, set of all elements $A$ .

Quantifiers to express what it means for a relation to be asymmetric is $\forall a \forall b ((a, b) \in R \to (b, a) \notin R)$ .

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Discrete Mathematics and its Applications

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Short Answer

Use quantifiers to express what it means for a relation to be asymmetric.

Step by Step Solution

Step 1: Given data

Step 2: Concept used of relation

Step 3: Solve for relation

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Discrete Mathematics and its Applications

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Short Answer

Use quantifiers to express what it means for a relation to be asymmetric.

Step by Step Solution

Step 1: Given data

Step 2: Concept used of relation

Step 3: Solve for relation

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