Question $1$: Design a Turing machine for the given language descriptions.

$[2$ marks$]$

$L=a^n{b}^{3n}$;$n>0.$

$L=a^{n+1}{b}^{n+3}$;$n0$

Question $2$: Do as directed. $[2$ marks$]$

Question $2$: Which languages do the following TMs represent?

Figure $1$: Language:

$()$

rgane a$.$ Lumgrungu.

Question $3$: In which state the string aaabbbcccc will be rejected by the TM in Figure $1?$

mark$]$