consider a $3-$bit integer a $=$ a$2$a$1$a$0$ and a $2-$bit integer b $=$ b$1$b$0.$ using the bits of a and b as your propositions $($so you have $5$ 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. Express your answers in wither conjunctive or disjunctive normal form

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

b$)$ a is divisible by $3$

c$)$ a $=$ b