How can I proof that if $\displaystyle L$ is a universal relation that $\displaystyle R total relation\equiv L = L \circ R$. It is pretty obvious that it is true, but how do I prove it?

Printable View

- Apr 2nd 2011, 11:35 AMgordo151091Total relation
How can I proof that if $\displaystyle L$ is a universal relation that $\displaystyle R total relation\equiv L = L \circ R$. It is pretty obvious that it is true, but how do I prove it?

- Apr 2nd 2011, 11:40 AMemakarov
Could you explain what Rtotalrelation is? Also, is universal relation the one that contains all possible pairs? Finally, by $\displaystyle L\cdot R$ do you mean the composition $\displaystyle L\circ R$?

- Apr 2nd 2011, 12:17 PMgordo151091
- Apr 3rd 2011, 02:49 AMPlato
This is just a matter of using the notation.

If $\displaystyle (a,b)$ is any pair then $\displaystyle \left( {\exists c} \right)\left[ {(c,b) \in R} \right]$ because $\displaystyle R$ is total.

Because $\displaystyle L$ is universal $\displaystyle (a,c)\in L$ so $\displaystyle (a,b)\in L\circ R.$ - Apr 3rd 2011, 10:34 AMemakarov
- Apr 3rd 2011, 11:05 AMPlato
Thanks, that is correct. It was either to early or the cut and paste.