a$)$ Assume L is a decidable language over the alphabet $\backslash$Sigma $.$ Let M be a Turing machine that decides L$,$ and let s$1,$ s$2,...,$ sk$,...$be a lexicographical ordering of the strings in $\backslash$Sigma $.$ Describe an enumerator that prints the strings in L in lexicographical order.

b$)$ Assume there exists an enumerator E for L that prints the strings in lexicographical order. Write a decider for L$.$ You may assume L is infinite. You can use pseudo$-$code for your decider.

c$)$ Would your decider still work if L is a finite language? Explain