| # | 0x0 | 0x1 | 1x0 | 1x1 | Logic | Simple | Gate | Alt | Venn | Symbols |
|---|---|---|---|---|---|---|---|---|---|---|
| [L] | 0 | 0 | 1 | 1 | ||||||
| [R] | 0 | 1 | 0 | 1 | ||||||
| 0 | 0 | 0 | 0 | 0 | Contradiction | 0 | FALSE |  |
⊥ | |
| 1 | 0 | 0 | 0 | 1 | Conjunction | L and R | AND | MIN |  |
∧ |
| 2 | 0 | 0 | 1 | 0 | Non-Implication | L and !R | NIMPLY | GT |  |
↛ > |
| 3 | 0 | 0 | 1 | 1 | Projection / Proposition of R | L | BUF |  |
||
| 4 | 0 | 1 | 0 | 0 | Converse Non-Implication | !L and R | LT |  |
↚ < | |
| 5 | 0 | 1 | 0 | 1 | Projection / Proposition of L | R | BUF |  |
||
| 6 | 0 | 1 | 1 | 0 | Exclusive Disjonction | L xor R | XOR | NEQ |  |
↮ ⊻ ≠ ⊕ |
| 7 | 0 | 1 | 1 | 1 | Disjonction | L or R | OR | MAX |  |
∨ |
| 8 | 1 | 0 | 0 | 0 | Joint Denial | !L or !R | NOR |  |
⊽ ↓ | |
| 9 | 1 | 0 | 0 | 1 | Biconditional | !( L xor R ) | XNOR | EQ |  |
↔ = ≡ |
| A | 1 | 0 | 1 | 0 | Negation of L | !R | NOT |  |
¬ | |
| B | 1 | 0 | 1 | 1 | Converse Implication | L or !R | GTE |  |
← ≥ | |
| C | 1 | 1 | 0 | 0 | Negation of R | !R | NOT |  |
¬ | |
| D | 1 | 1 | 0 | 1 | Implication | !L or R | IMPLY | LTE |  |
→ ≤ ⊃ |
| E | 1 | 1 | 1 | 0 | Alternative Denial | !L and !R | NAND |  |
⊼ ↑ | |
| F | 1 | 1 | 1 | 1 | Tautology | 1 | TRUE |  |
⊤ | |
| [L] | 0 | 0 | 1 | 1 | ||||||
| [R] | 0 | 1 | 0 | 1 |
Legend:
- Italic for Non-Binary Operatiors
- Bold for Commutative Operators