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**mukesh****Member**- Registered: 2010-07-18
- Posts: 30

sir,if A is a set such tht A=$1,2,3$ and R=[(1,1),(2,2),(1,3)] is it transitive relation?plse explain,

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

I'd say so.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

???

Is R the relation

1 --> 1

2 --> 2

1 --> 3

because that doesn't look right to me.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

No, the relation R is {{1,1},{2,2},{1,3}}, like it says.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

Sorry. maybe I'm just thick; but how is that a relation? It just looks like a set of ordered pairs.

This is what I think of when I've got a relation:

eg. A = (1,2,3} B = (1,4,9} A is related to be by (element in A)^2 = (corresponding element in B)

Please spell it out for me.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

What you are thinking of is an operation.

A relation is something like =,<=,>=,...

For example, on the set {1,2,3} you can define = as {(1,1),(2,2),(3,3)], i.e., the set of ordered pairs for which the relation holds.

Also,

> : {(2,1),(3,1),(3,2)}

< : {(1,2),(1,3),(2,3)}

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

OK. Thanks. I'm going to use --> to mean 'is related to'

So

1 --> 1

2 --> 2

1 --> 3

looks to me like another way to describe the relation.

Then to test for transitivity I must check out all the three way combinations:

1 --> 1 -->1 Is it true that element 1 --> element 3 ? Yes, because 1 --> 1

1 --> 1 -->3 Is it true that element 1 --> element 3 ? Yes, because 1 --> 3

2 --> 2 -->2 Is it true that element 1 --> element 3 ? Yes, because 2 --> 2

1 --> 3 -->? 3 --> is undefined.

There are no more triples so I have, by exhaustion, tested and proved transitivity for this relation.

How does that sound?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Sounds okay.

Here lies the reader who will never open this book. He is forever dead.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

Thanks. I'm happy now.

Bob

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

No problem. Of, course, the standard relartion notation is to use the name of the relation, e.g.:

To note that 1 is related to 3 with respect to the relation R, you'd say 1R3. It's like if you said 1<3.

Here lies the reader who will never open this book. He is forever dead.

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