(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A is some set.

R is a relation (set of ordered pairs), and is transitive on A.

S = {(x,y) | (x,y) is element of R, (y,x) is not element of R}

Show that S is transitive and trichotomic on A.

2. Relevant equations

Transitivity: With xRy and yRz ==> xRz

3. The attempt at a solution

For all x, y, z element of A : xRy and yRz ==> xRz

and for all a, b, c element of A: aRb and bRc ==> aRc

Now my problem: when I want to show transitivity from S on A, how can I be sure that c != x and a != z, because S is defined as (x,y) element R but not (y, x).

It would be nice if someone could write out the solution for this problem in full. I need a good example to hold on to when trying to solve other problems. I hope I don't ask for to much...

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# Homework Help: Set Theory, relations, transitivity

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