A + 1 = 1 — Boolean algebra laws
edge caseannulment / null element
Answer
verified equivalent (both sides → 1)
Why this example is worth doing
The annulment law, paired on the page with its dual A·0 = 0 and carefully distinguished from the identity laws A + 0 = A and A·1 = A. Four short identities, and mixing them up is the most common source of a derivation that goes wrong in its second line. The page sets all four in one table with the operator and the constant as the two axes, which makes the pattern — the constant that matches the operator's dominant element wins — visible instead of memorised.
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 + 11— Both sides have the same truth table over the union of their variables.
Truth table
| # | A | F |
|---|---|---|
| 0 | 0 | 1 |
| 1 | 1 | 1 |