For the logical system that we $($and essentially everyone$)$ use, lets use the notation $($M$,\backslash$Phi $,=,,,)$

to mean that M is the set of statements we work with, $\backslash$Phi is the function that assesses truth, and the

others are the logical operations and operator.

Please prove or disprove that the our logical system $($M$,\backslash$Phi $,=,,,)$ can be replaced with $($M$,\backslash$Phi $,),$

where $$ is defined as follows. For x$,$ y in M$,$ x $$ y is equivalent to $($x $$ y$)$