# Thread: discrete math relations simple problem help !!!!

1. ## discrete math relations simple problem help !!!!

Let A = {(x, y) | x, y integers}. Define a relation R on A by the rule (a, b) R (c, d) ↔ a = c or b = d. Determine whether R is transitive.
I know that it's not transitive but how to prove that is my problem.
shall I prove it with an example with numbers or with letters???!!!

2. ## Re: discrete math relations simple problem help !!!!

Originally Posted by ujnikm
Let A = {(x, y) | x, y integers}. Define a relation R on A by the rule (a, b) R (c, d) ↔ a = c or b = d. Determine whether R is transitive.
I know that it's not transitive but how to prove that is my problem.
shall I prove it with an example with numbers or with letters???!!!

You give a counterexample. But it must be done with integers.

$\displaystyle (1,3)R(1,2)~\&~(1,2)R(4,2)$ BUT ?

3. ## Re: discrete math relations simple problem help !!!!

Originally Posted by Plato
You give a counterexample. But it must be done with integers.

$\displaystyle (1,3)R(1,2)~\&~(1,2)R(4,2)$ BUT ?
can u illustrate more ??? please

4. ## Re: discrete math relations simple problem help !!!!

Originally Posted by ujnikm
can u illustrate more ??? please
What do you mean. It is clear.

$\displaystyle (1,3)R(1,2)~\&~(1,2)R(4,2)$ BUT NOT $\displaystyle (1,3)R(4,2)$