Construct a DFA (deterministic finite state machine)

1. {0,1}* the binary encoding of a positive integer that is divisible by 7

2. {0,1,2,,9}* the decimal encoding, without leading 0s, of an odd natural number

Construct a NFA (non-deterministic finite state machine)

1. {w contains {a,b,c,d,e}* : 1st symbol of w the last symbol}

2. {w contains {0,1,2,,9}* : w corresponds to the decimal encoding, without leading 0s, of an odd natural number}

3. {w contains {0-9}* : w contains a substring that is divisible by 3}. For example, 32, 1115, 101, 14278 are in the language, but 22, 47 are not.