Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

Login

Username

Password

Not registered yet?

#1 2013-07-03 05:08:08

mukesh
Member

Offline

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,

#2 2013-07-03 05:35:07

anonimnystefy
Real Member

Online

Re: set relation

I'd say so.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#3 2013-07-03 05:55:19

bob bundy
Moderator

Offline

Re: set relation

???

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

#4 2013-07-03 06:10:52

anonimnystefy
Real Member

Online

Re: set relation

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#5 2013-07-03 06:20:46

bob bundy
Moderator

Offline

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


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

#6 2013-07-03 06:23:58

anonimnystefy
Real Member

Online

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)}


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#7 2013-07-03 06:38:18

bob bundy
Moderator

Offline

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


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

#8 2013-07-03 06:39:15

anonimnystefy
Real Member

Online

Re: set relation

Sounds okay.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#9 2013-07-03 06:40:44

bob bundy
Moderator

Offline

Re: set relation

Thanks.  I'm happy now.  smile

Bob


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

#10 2013-07-03 23:25:09

anonimnystefy
Real Member

Online

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.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Board footer

Powered by FluxBB