(A + B)′ — De Morgan's laws
introNOR expands to a product
Answer
A′ · B′
Why this example is worth doing
The dual half, and the more frequently mangled one. (A + B)′ is Ā·B̄ and not Ā + B̄, and the page shows the disagreement row by row: the wrong answer is right only when A and B are both 0. Presenting the error explicitly rather than only the correct result is deliberate — students recognise their own mistake faster than they absorb a rule. The NOR gate page reuses this expansion to justify the inverted-input AND symbol.
Try your own input in the De Morgan’s laws. Push a negation through any expression and see both forms side by side.
How the answer is reached
Negation pushed inwards
(A + B)′A′ · B′— De Morgan swaps the operator as the bar passes through it.
Truth table
| # | A | B | F |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 2 | 1 | 0 | 0 |
| 3 | 1 | 1 | 0 |