$[6$ 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 $$ perator. In each case, prove that your expressions are equivalent using

Boolean algebra.