$2\mathrm{.}21.$ For each of the following languages Lsube$\{a,b{\}}^{**},$ show that the elements of the infinite set $\{a^n|n0\}$ are pairwise $L-$distinguishable.

a$.L=\{a^{n}b{a}^{2n}|n0\}$

b$.L=\{a^i{b}^j{a}^k|k>i+j\}$

c$.|=i$ or $\{$:$j=2i\}$

d$.|)$:$\}$ is a multiple of $\{$:$i\}$