Q$2$ Identify the regular languages

$2$ Points

For each of the following languages state whether it is regular or not. If $L_i$ is regular, prove it by

drawing either a DFA or an NFA that recognizes it$.$

If the language is not regular, give an argument in plain language why there is no DFA or NFA that

can recognize it$.$

For each question, assume $=\{a,b\}.$

Q$2\mathrm{.}1$ L$\_$a

$0\mathrm{.}5$ Points

$L_a=\{ww{a}^n$:win$\{a,b\},n>0\}$

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Q$2\mathrm{.}2$ L$\_$b

$0\mathrm{.}5$ Points

$L_b=\{b^{n}ww$:win$\{a,b\},n0\}$

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Q$2\mathrm{.}3$ L$\_$C

$0\mathrm{.}5$ Points

$L_c=\{axy$:$x,$yin$\{a,b{\}}^{**}\}$

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Q$2\mathrm{.}4$ L$\_$d

$0\mathrm{.}5$ Points

$L_d=\{wawa$:win$\{a,b{\}}^{**}\}$

Please select file$($s$)$