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:
“There is all the poetry in the world in a name. It is a poem which the mass of men hear and read. What is poetry in the common sense, but a hearing of such jingling names? I want nothing better than a good word. The name of a thing may easily be more than the thing itself to me.”
—Henry David Thoreau (1817–1862)
“The logical English train a scholar as they train an engineer. Oxford is Greek factory, as Wilton mills weave carpet, and Sheffield grinds steel. They know the use of a tutor, as they know the use of a horse; and they draw the greatest amount of benefit from both. The reading men are kept by hard walking, hard riding, and measured eating and drinking, at the top of their condition, and two days before the examination, do not work but lounge, ride, or run, to be fresh on the college doomsday.”
—Ralph Waldo Emerson (1803–1882)