15) Let M be the language over {a, b, c, d, e, f} accepting all strings so that: 1. There are precisely two e's in the string. 2. Every a is immediately followed by an even number of b's. 3. Every c is immediately followed by an odd number of f's. 4. b's and f's don't occur except as provided in rules 2 and 3. 5. All c's occur after the first e. 6. All a's occur before the second e. 7. In between the two e's there are exactly twice as many c's as a's.

Just need questions 4,5,6

Let E= {a, b}. Given regular expressions r = a*b*, r' = ba(ab)* + ab*ba* and r" = (a + b)aa(a + b)*, find L(r), L(r'), and L(r"), the languages defined by r, r', r", respectively.

1. {w E {0, 1} *: w begins with 1 and, when interpreted as a binary number, is a multiple of 5} (since this DFA uses alphabet {0,1}, please flip our conventions and use states a, b, c, ...). *NOTE: Also include the language accepted by DFA as a set. 2. {w| w starts with an a and has at most one b} Draw DFA for each and make intersection of them. i.e, a. 1 DFA for start with an a b. 1 DFA for has at most one b c. 1 DFA for intersection of both of a and b