1. (10 points) In parts (a) and (b) the alphabet is {0,1}.

(a) Give the state diagram of a DFA recognizing the language L1 = {w|w represents a binary number that has remainder 1 or 3 when divided by 7}(with as few states as you can). Leading 0s should be ignored. The empty string can be accepted or rejected it is up to you.

(b) Give the state diagram of an NFA recognizing the language L3 = {w | w contains substrings 1000 and 10 which do not overlap} (with as few states as you can).