- #1

mr_coffee

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**Binary Relations--Transitivity**

Hello everyone I'm not sure if I'm hitting all the ordered pairs on this because i can't seem to find a good method to figure it out. I also think the relation to itself is confusing me.

here is the question:

S is a binary relation defined on A = {0,1,2,3}

to speed up this message, I'm going to represent an ordered pair like 00 instead of (0,0).

Let S = {00, 03, 10, 12, 20, 32}

Find S^t, the transititve closure of S.

note: ... 32 .. stands for (3,2), etc

Okay i know for somthing to be transitive, if you have an arrow from point 0 to 0, then it has a relation to itself..

Also

If i had say a relation like (0,1) and (1,2) then I can make an ordered pair from (0,2).

Thats what I'm doing in this problem

So i got the following but I'm not sure if I'm right.

S^t = S UNION { 11, 33, 22, 30, 01, 02 13, 31}

Thanks.