$[$a$]$ Explain what is meant by the "functional completeness" of a set of Boolean operators.

$[$b$]$ Prove that the operator set $\{$NOT$,$ AND, OR$\}$ is functionally complete. Hint: how is this related to Q$1?$

$[$c$]$ Prove that the operator set $\{$NOT$,$ OR$\}$ is functionally complete.

$[$d$]$ Prove that the operator set $\{$NOT$,$ AND$\}$ is functionally complete.

$[$e$]$ Prove that the operator set $\{$NAND$\}$ is functionally complete.