Equivalence and DFA$$s

Let M be any DFA and let X $=$ L$($M$).$ Then it is possible that there exist two strings u and v such that u and v are X$-$equivalent, but that M takes u and v to different states $($that is$,\backslash$delta $*($i$,$ u$)!=\backslash$delta $*($i$,$ v$)).$ true or false