Are the following languages A and $B$ over the alphabet $=\{a,b,c,d\}$ regular or nonreg$-$

ular?

For a language that is regular, give a regular expression that defines it$.$

For a nonregular language, using the pumping lemma prove that it is not regular.

$($a$)(2$ marks$)$

$A=\{a^{3i}{b}^k{c}^m{d}^{2k}|i0,k0,m0\}$

$($b$)(2$ marks$)$

$B=\{a^{j+5}{b}^{k+3}{c}^{m+1}|j1,k1,m1\}$

$\{b^r{c}^{2s+3}{d}^{t+1}|r1,s1,t1\}.$