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

You are not logged in.

## Post a reply

Write your message and submit
|
Options

## Topic review (newest first)

anonimnystefy
2013-07-03 23:25:09

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.

bob bundy
2013-07-03 06:40:44

Thanks.  I'm happy now.

Bob

anonimnystefy
2013-07-03 06:39:15

Sounds okay.

bob bundy
2013-07-03 06:38:18

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

anonimnystefy
2013-07-03 06:23:58

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)}

bob bundy
2013-07-03 06:20:46

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

anonimnystefy
2013-07-03 06:10:52

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

bob bundy
2013-07-03 05:55:19

???

Is R the relation

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

because that doesn't look right to me.

Bob

anonimnystefy
2013-07-03 05:35:07

I'd say so.

mukesh
2013-07-03 05:08:08

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,