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:
“You common cry of curs, whose breath I hate
As reek a’th’rotten fens, whose loves I prize
As the dead carcasses of unburied men
That do corrupt my air—I banish you!”
—William Shakespeare (1564–1616)
“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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