Solved Problem - Truth tables
Question
Prove de Morgan's theorems
and
with the use of truth tables.
Answer
For the first expression the relevant truth table is given below, the equivalence between the entries in the red columns prove the first theorem.
 |  |
 | 
| .
| +
|  |
| 0 | 0 | 1 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 | 0 | 1 | 0 |
The truth table for the second expression is given below, again the two columns proving the theorem are highlighted in red.
| |
|
| +
| .
|  |
| 0 | 0 | 1 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 0 | 1 | 0 |
