Section $1\mathrm{.}7$

$11.$ Let $\backslash$Sigma $=\{$a$1,...,$a$26\}$ be the Roman alphabet. De ne the binary rela

tion $<$ on $\backslash$Sigma $$ such that x $<$ y if and only if x would precede y in a standard

dictionary.

$12.$ Prove that $\{$e$\}=\{$e$\}.$

$13.$ Prove that for any alphabet $\backslash$Sigma and any L $\backslash$Sigma $,$ we have $($L$)=$ L$$