$[6$ marks$]$ The Boolean operator NOR $(darr)$ is functionally complete. This means that you can write a Boolean expression using one or more NOR operators that produces the same truth table as each of the logical operators AND, OR$,$ and NOT.

For each of these three operators ${?}^{{?}^{?}}(v,$ fiwrite a Boolean expression that is equivalent using only the eperator. In each case, prove that your expressions are equivalent using Boolean algebra.

Submit the file a$1$q$4.$pdf$.$