   Chapter 8.5, Problem 3ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Let S be the set of all strings of a’s and b’s. Define a relation R on S as follows: For every s , ​   t ∈ S , s   R   t ⇔ L ( s ) ≤ L ( t ) , where L(x) denotes the length of a string x. Is R antisymmetric? Prove or give a counterexample.

To determine

To check:

Whether R is antisymmetric or not.

Explanation

Given information:

Let S be the set of all strings of a's and b's. Define a relation R on S as follows:

For all tS,sRtI(s)I(t).

Concept used:

A relation R on a set A is said to be antisymmetric if and only if for all a and b in A, if aRb and bRa then a=b.

Calculation:

Suppose S be the set of all strings of a's and b's.

Define a relation R on S as follows.

For all s,tS, sRtI(s)I(t).

Here, I(x) denotes the length of a string x.

The objective is to determine whether the relation R is antisymmetric or not.

A relation R on a set A is said to be antisymmetric if and only if for all a and b in A, if aRb and bRa then a=b

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