The Myhill$-$Nerode Equivalence Relation

Let L be any language, and let u and v each be strings that cannot be extended into L$.$ That is$,$ for any string z$,$ neither uz nor vz is in L$.($So since z could be $\backslash$lambda $,$ neither u nor v is in L$.)$ Then u and v are L$-$equivalent strings. true or false