a$)$ The Boolean expression $+$

$$ a$\mathrm{.}1)$ is representing the XOR function.

$$ a$\mathrm{.}2)$ is equal to the Boolean expression $.$

$$ a$\mathrm{.}3)$ is equal to the Boolean expression $+.$

$$ a$\mathrm{.}4)$ is representing the NOR function.