Consider the binary alphabet; give a DFA for each of the following languages:

a$.$ All binary strings with at least three ones

b$.$ All binary strings with an odd number of ones

c$.$ All binary strings without $111$ as a substring

d$.$ All binary strings where every odd position is a $1($positions are numbered from $1$ and

up$)$

e$.$ All binary strings with exactly three $1\text{'}$s

f$.$ All binary strings that have at least three symbols and whose first and last symbols

are different