Common Logical Connectives
| Name / Symbol | Truth table | Venn | |||||
|---|---|---|---|---|---|---|---|
| P = | 0 | 1 | |||||
| Truth/Tautology | ⊤ | 1 | 1 | ||||
| Proposition P | 0 | 1 | |||||
| False/Contradiction | ⊥ | 0 | 0 | ||||
| Negation | ¬ | 1 | 0 | ||||
| Binary connectives | P = | 0 | 0 | 1 | 1 | ||
| Q = | 0 | 1 | 0 | 1 | |||
| Conjunction | ∧ | 0 | 0 | 0 | 1 | ||
| Alternative denial | ↑ | 1 | 1 | 1 | 0 | ||
| Disjunction | ∨ | 0 | 1 | 1 | 1 | ||
| Joint denial | ↓ | 1 | 0 | 0 | 0 | ||
| Material conditional | → | 1 | 1 | 0 | 1 | ||
| Exclusive or | 0 | 1 | 1 | 0 | |||
| Biconditional | ↔ | 1 | 0 | 0 | 1 | ||
| Converse implication | ← | 1 | 0 | 1 | 1 | ||
| Proposition P | 0 | 0 | 1 | 1 | |||
| Proposition Q | 0 | 1 | 0 | 1 | |||
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Famous quotes containing the words common and/or logical:
“All this class of pleasures inspires me with the same nausea as I feel at the sight of rich plum-cake or sweetmeats; I prefer the driest bread of common life.”
—Sydney Smith (1771–1845)
“It is merely a linguistic peculiarity, not a logical fact, that we say “that is red” instead of “that reddens,” either in the sense of growing, becoming, red, or in the sense of making something else red.”
—John Dewey (1859–1952)
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