There are 256 possible output columns for truth tables involving only P,Q, and R. For each of the 256 possible columns, find a logical statement with (any number of) P, Q, R, ∧, ∨, =⇒ , ⇔, ¬ that outputs that column.

1. Hint: Try special cases and prove useful lemmas along the way. Aim for a solution that fits on one page.)