$($b$)(1$ pt$)$ With AND, OR$,$ XOR, IF$-$THEN, and your new operation we have defined $5$ distinct operations. How many distinct logical binary operations are there? Just $5?6,?$ Somewhere in$-$between? Here I am not looking for a proof, but we need to see an explanation of how you came upon your answer $($Note binary operations are the same if for every input they give the same output and they are distinct if for some input they give different outputs$).$