Logic/De Morgan's laws
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Logic > De Morgan's laws
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Overview
Definition of De Morgan's laws by truth table
0 means false, 1 means true, and ≡ means equivalent.
Case of "￢(P∧Q)" ≡ "￢P∨￢Q".
| P | Q | P∧Q | ￢P | ￢Q | ￢P∨￢Q | ￢（P∧Q） |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 0 | 0 |
Case of "￢(P∨Q)" ≡ "￢P∧￢Q".
| P | Q | P∨Q | ￢P | ￢Q | ￢P∧￢Q | ￢（P∨Q） |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 1 | 0 | 0 | 0 | 0 |
