Math Is Fun Forum

mukesh

Member

Registered: 2010-07-18

Posts: 31

set relation

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,

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: set relation

I'd say so.

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“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
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: set relation

???

Is R the relation

1 --> 1
2 --> 2
1 --> 3

because that doesn't look right to me.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: set relation

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
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: set relation

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

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: set relation

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
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: set relation

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

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: set relation

Sounds okay.

---

“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
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: set relation

Thanks.  I'm happy now. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: set relation

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.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.