$[6$ 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 $,$ tiwrite a Boolean expression that is equivalent using only the $\backslash$Phi perator. In each case, prove that your expressions are equivalent using Boolean algebra.