(A′)′ = A — Boolean algebra laws

Why this example is worth doing

Double negation, the shortest law on the page and the one that quietly does the most work. Every De Morgan manipulation ends by cancelling a pair of bubbles, and the bubble-pushing technique used on the gate diagram pages is nothing but involution applied graphically: two inversions on the same wire annihilate. The page draws that equivalence between the algebra and the schematic explicitly, because students who have learned bubble pushing as a drawing trick often do not connect it to a law they already know.

Try your own input in the Boolean laws & theorems. Every law, both duals, each with a truth-table proof you can check.