A + Ā = 1 — Boolean algebra laws
corecomplement / excluded middle
Answer
verified equivalent (both sides → 1)
Why this example is worth doing
The complement law, which together with the identity, null, idempotent and commutative laws forms the axiom set everything else is derived from. The page shows the two-row proof and then does something more useful: it traces which later results depend on it. Adjacency, absorption and the whole of K-map grouping all bottom out here. Presenting the axioms as a dependency graph rather than a flat list is the main thing this reference does that a textbook appendix does not.
Try your own input in the Boolean laws & theorems. Every law, both duals, each with a truth-table proof you can check.
How the answer is reached
The law
A + A′1— Both sides have the same truth table over the union of their variables.
Truth table
| # | A | F |
|---|---|---|
| 0 | 0 | 1 |
| 1 | 1 | 1 |