Transitivity

Mephisto

Mephisto

Mephisto

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Ok I'm doing a Maths assignment atm, and I missed a 2 hour lecture on the stuff that we're doing in this assignment so I'm trying to catch up and do the assignment at the same time. I'm doing fine so far except for one thing: transitivty. I just don't understand how it works.

The definintion of transitivity is
dbd38170267672ffb14a610un7.png


Now I understand this, but I don't understand how to apply it to sets with more than three elements. I was looking through the book we've got and there's one example:

S = {0,1,2,4,6}

R1 = {(0,0),(1,1),(2,2),(4,4),(4,6),(6,6),(6,4)}

According to the book R1 is transitive, but I don't understand why. Can anyone shed some light on this please? And explain it a bit further because I'm not sure how it works in sets with more than 3 elements as in the definition.

Thanks
 
That's not transitive - every element needs to be able to get to the other...which I'm sure that in R1 it can't, i.e. 0 can't get to 6 etc.
 
Last edited:
I remember doing this last year, where you studying/what?

The 2nd element of a pair points to the first element of another pair. If a set is transitive all the elements are involved in loops.

So in this case (1,1) points to itself and so do all the other set with identical items.

and then (4,6) points to (6,4) which points back, therefore loop.

I think thats right but check your notes, or can you post the actual question you've been set? This is good revision for me haha.
 
Ok well I've realised the actual assignment doesn't have weird relations like the one I wrote in the OP, which I still find confusing. I should be ok, thanks for the help.

I'm doing a software development/computer programming course, and part of that is this unit called Mathematics for computing.
 
Mephisto said:
Ok I'm doing a Maths assignment atm, and I missed a 2 hour lecture on the stuff that we're doing in this assignment so I'm trying to catch up and do the assignment at the same time. I'm doing fine so far except for one thing: transitivty. I just don't understand how it works.

The definintion of transitivity is
dbd38170267672ffb14a610un7.png


Now I understand this, but I don't understand how to apply it to sets with more than three elements. I was looking through the book we've got and there's one example:

S = {0,1,2,4,6}

R1 = {(0,0),(1,1),(2,2),(4,4),(4,6),(6,6),(6,4)}

According to the book R1 is transitive, but I don't understand why. Can anyone shed some light on this please? And explain it a bit further because I'm not sure how it works in sets with more than 3 elements as in the definition.
Click to expand...
Basically the definition is saying that if (x,y) \in R1 and (y,z) \in R1, then (x,z) \in R1.

So just by brute force there are 49 possibilities to check.

But notice that you can ignore the case where the first pair (x,y) has x=y, because if you have x=y, then it's obvious that (x,y) \in R1 and (y,z) \in R1 means that (x,z) in R1.

That cuts it down to just a few possibilities to check:

(x,y) = (4,6) (y,z) = (6,4). Then (x,z) = (4,4) which is in R1.
(x,y) = (4,6) (y,z) = (6,6). Then (x,z) = (4,6) which is in R1.
(x,y) = (6,4) (y,z) = (4,6). Then (x,z) = (6,6) which is in R1.
(x,y) = (6,4) (y,z) = (4,4). Then (x,z) = (6,4) which is in R1.

So in every case where (x,y) and (y,z) are in R1, we also have (x,z) in R1, so it's transitive.
 
Amleto said:
never did this and I did 4 years of applied maths so it can't be that useful :p
Click to expand...

its discrete math used in computing, the set structure is useful but ive not learnt anything that actually applies the more complex stuff, roll on Discrete maths two in january.
 
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