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 | |||
| More information | |||||||
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Famous quotes containing the words common and/or logical:
“... exchanging platitudes, as Frenchmen do, for the pleasure of feeling their mouths full of the good meat of common sense.”
—Rebecca West (1892–1983)
“Grammar is a tricky, inconsistent thing. Being the backbone of speech and writing, it should, we think, be eminently logical, make perfect sense, like the human skeleton. But, of course, the skeleton is arbitrary, too. Why twelve pairs of ribs rather than eleven or thirteen? Why thirty-two teeth? It has something to do with evolution and functionalism—but only sometimes, not always. So there are aspects of grammar that make good, logical sense, and others that do not.”
—John Simon (b. 1925)
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