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?
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?
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 $\displaystyle (a,b)\in L\circ R.$