1. Construct a DFA for the set of binary strings that begin with 1 or end in 101.
2. Construct a DFA for the set of binary strings that have a zero at 3 or 5 places from the end of the string.
3. Construct a DFA that is equivalent to the NFA below:
$\epsilon, a$
$a,b$
$\epsilon, b$
$a,b$
$a$
$b$
$a,b$
$a$
4. Construct an NFA for the regular expression ab(bab)* + ab*ab*
5. Construct an equivalent regular expression for the NFA below:
$b$
$b, \epsilon$
$a, \epsilon$
$a$
$a,b$
$b$
$a$