| x | y | ~x | ~y | x & y | ~(x & y) | ~x | ~y | ~~x |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |
This verifies the first version of DeMorgan's Law below and the idempotent law (~~x = x) for single bit values x and y.
~(x & y) = (~x) | (~y)
~(x | y) = (~x) & (~y)
~~x = x
These DeMorgan's Laws for single bit values are analogous the following version applied to logical statements p, q with values true corresponding to 1 and false corresponding to 0:
The following are logical statements equivalent
- It is not the case that both p and q are true
- Either p is not true or q is not true
Symbolically
NOT (p AND q) = (NOT p) OR (NOT q)
and similarly
NOT (p OR q) = (NOT p) AND (NOT q)