| Identity | |
|---|---|
| A | A |
| 0 | 0 |
| 1 | 1 |
| Negation | |
|---|---|
| ¬A | A |
| 0 | 1 |
| 1 | 0 |
| AND - conjunction | ||
|---|---|---|
| A | B | A ^ B |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
| NAND | ||
|---|---|---|
| A | B | A ↑ B |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
| OR - disjunction | ||
|---|---|---|
| A | B | A V B |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
| NOR | ||
|---|---|---|
| A | B | A ↓ B |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
| EQUALS | ||
|---|---|---|
| A | B | A == B |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
| Implication - conditional if - then | ||
|---|---|---|
| A | B | A → B |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
| N Implication - conditional then - if | ||
|---|---|---|
| A | B | A → B |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
| XOR - exclusive or | ||
|---|---|---|
| A | B | A ⊕ B |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
| NXOR - exclusive nor - biconditional - if and only if | ||
|---|---|---|
| A | B | A B |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
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