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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.

To determine

An example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.

Explanation

Formula Used:

(1) A relation R on a nonempty set A is reflexive if the following property is satisfied:

xRx for all xA.

(2) A relation R on a nonempty set A is symmetric if the following property is satisfied:

If xRy, then yRx.

(3) A relation R on a nonempty set A is transitive if the following property is satisfied:

If xRy and yRz, then xRz.

Explanation:

Consider the relation R on the set A {a,b} defined as xRy if and only if R={(a,a)}

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