Q$2$ Languages

$18$ Points

Answer the following questions on this collection of languages. Recall that $n_x(w)$ means "the

number of $x^{\text{'}}$ s in $w^{\text{'}\text{'}}.$

$L1=\{,a,b,aa\},=\{a,b\}$

$L2=\{b,bb,$bba$\},=\{a,b\}$

$L3=\{ww|win{}^{+}\},=\{b\}$

$L4=(aa{)}^{*}(bb{)}^{*},=\{a,b\}$

$L5=\{win{}^{*}|n_a(w)>n_b(w)\},=\{a,b\}$

Q$2\mathrm{.}1$ a

$3$ Points

$L_2{L}_3=$