A + A·B = A — Boolean algebra laws
introabsorption
Answer
verified equivalent (both sides → A)
Why this example is worth doing
Absorption gets its own worked page because it is the law students can state and still fail to apply. The page proves it three ways — by truth table, by factoring through the annulment law, and by K-map, where A·B is a sub-rectangle of the A rectangle and adds no area. The geometric reading is the one that tends to stick: absorption is what it looks like when one group is entirely inside another, and its dual A·(A + B) = A is the same picture in the OFF-set.
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 · BA— Both sides have the same truth table over the union of their variables.
Truth table
| # | A | B | F |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 2 | 1 | 0 | 1 |
| 3 | 1 | 1 | 1 |