Exercise $27$ Equivalence of Words

$(8$ points$)$

In this exercise the equivalence of words according to the Myhill$-$Nerode equivalence shall be examined. Justify the correctness of your answers!

$($a$)$ Let the language $L_1=\{(abc{)}^n|nin{N}_0\}$ over the alphabet $=\{a,b,c\}$ be given. In the following we use the Myhill$-$Nerode equivalence $-={?}_{L_1}.$

Give one equivalent word for each of the following words: $a,c$ and abc. Also give a word which is not equivalent to any of these three words.

Write down the equivalence class which contains the word a and the equivalence class which contains the word $abc$ in set notation.