De Morgan's laws
In boolean algebra, DeMorgan's laws are the laws of how a NOT gate affects AND and OR statements:[1]
They can be remembered by "break the line, change the sign".
Truth tables
The following truth tables prove DeMorgan's laws.
| INPUT | OUTPUT 1 | OUTPUT 2 | |
| A | B | NOT (A AND B) | (NOT A) OR (NOT B) |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| INPUT | OUTPUT 1 | OUTPUT 2 | |
| A | B | NOT (A OR B) | (NOT A) AND (NOT B) |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 |
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