iven a $3-$bit integer a $=$ a$2$a$1$a$0$ and a $2-$bit integer b $=$ b$1$b$0,$ use the bits of a and b as your propositions $($with $5$ atomic propositions: a$0,$ a$1,$ a$2,$ b$0,$ and b$1,$ where $0$ indicates false and $1$ indicates true$).$ Write a propositional logic formula for each of the following claims and express your answers in either conjunctive or disjunctive normal form:

$($a$)($a $+$ b$)$ is odd.

$($b$)$ a is divisible by $3.$

$($c$)$ a $=$ b$.$