Assignment 1: Build DFAs that accept certain languages and meets certain requirements

I"m not great at building DFAs and any help would be appreciated, especially Problem #3.

Grec x Conx (23) XD (23) X Mec x IEEE IEEE X C ProL x C 2 X 355 x CIW x Th Coux ? C Get X + c File C:/Users/John/Downloads/assignment01521.pdf 10 assignmento1S21.pdf 1/1 200% DUE DATE: FEBRUARY 19 AT 10:00 PM (1) Build a DFA which only accepts the following languages on = {a,b}: (a) L = {w: W mod 5 + 0} (b) L = {wina(w) mod 3> 1} (2) Build a DFA which only accepts the following languages on S = {0,1}: (a) The set of all strings in which every 0.0 is followed immediately by a 1. For example the string 1.0.1, 1.0.0.1, 0.0.1.1, 0.0.1.1.0.1.0.0.1 are in the language, but 0.0.0.1 and 0.0.1.0.0 are not. (b) The set of all strings with the leftmost two symbols are identical to the right most two symbols. 1 (3) Let S = { 0 1}. A string of symbols in I gives three rows of O's and i's. Consider each row to be a binary number. Build a DFA which only accepts the language L = {we * : the bottom row of w is the sum of the top two rows. Hint: Working with LR is easier. (LR is the reversed language that accepts the reversed sentences of L. Also, the string a.b.c" is the reverse of "c.b.a") Type here to search A d) 3:34 PM 2/18/2021 Grec x Conx (23) XD (23) X Mec x IEEE IEEE X C ProL x C 2 X 355 x CIW x Th Coux ? C Get X + c File C:/Users/John/Downloads/assignment01521.pdf 10 assignmento1S21.pdf 1/1 200% DUE DATE: FEBRUARY 19 AT 10:00 PM (1) Build a DFA which only accepts the following languages on = {a,b}: (a) L = {w: W mod 5 + 0} (b) L = {wina(w) mod 3> 1} (2) Build a DFA which only accepts the following languages on S = {0,1}: (a) The set of all strings in which every 0.0 is followed immediately by a 1. For example the string 1.0.1, 1.0.0.1, 0.0.1.1, 0.0.1.1.0.1.0.0.1 are in the language, but 0.0.0.1 and 0.0.1.0.0 are not. (b) The set of all strings with the leftmost two symbols are identical to the right most two symbols. 1 (3) Let S = { 0 1}. A string of symbols in I gives three rows of O's and i's. Consider each row to be a binary number. Build a DFA which only accepts the language L = {we * : the bottom row of w is the sum of the top two rows. Hint: Working with LR is easier. (LR is the reversed language that accepts the reversed sentences of L. Also, the string a.b.c" is the reverse of "c.b.a") Type here to search A d) 3:34 PM 2/18/2021