A·(A + B) = A — Boolean algebra laws
exam standarddual of absorption
Answer
verified equivalent (both sides → A)
Why this example is worth doing
The dual of absorption, and the entry point for the duality principle itself: swap every AND with OR and every 0 with 1 in any valid identity and the result is also valid. That single observation halves the number of laws to memorise, and the page presents the whole axiom set in dual pairs for that reason. The caution it also carries is that the dual of an expression is not its complement — f^d(x) = f′(x̄) — which is the confusion that produces wrong minimal POS results.
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 + B)A— 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 |