$1\mathrm{.}99$ Consider the following regular languages over binary alphabet $\{0,1\}$ Li$=\{$ number w is a multiple of $3\},$ L$2=$ w$=$wiW$2...$Wn $(-1)*$wk is a multiple of $3$ k$=1\{$v $---\}\}$ L$3=$ W$=$WnWn$-1...$W$1(-1)\{$wis a multiple of $3$ k$=1$ a$)$ Identify manually which of these numbers are multiples of $3$: $($Each line is a single number. I broke it down in blocks of $6$ bits for readability.$)1)1010101010110101001110101101101101010101011011111011012)1111111111111111111110111101111011111101111111101111113)1000010000001000000000010000000000100000001000000101014)110011001100110011001100110011001100110011001100110011$ b$)$ c$)$ Prove that L$1=$ L$2=$L$3.$ Explain the link with the automaton seen in class: M$3,20191$