Exercise $2\mathrm{.}2\mathrm{.}5$: Give DFA's accepting the following languages over the alphabet $\{$O$,1\}$:

a$)$ The set of all strings such that any five consecutive symbols contains

at least two O$\text{'}$s$.$

b$)$ The set of all strings whose tenth symbol from the right end is a $1.$

c$)$ The set of strings that either begin or end $($or both$)$ with $01.$

d$)$ The set of strings such that the number of O$\text{'}$s is divisible by five, and the

number of $1\text{'}$s is divisible by $3.$