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:
“When we are high and airy hundreds say
That if we hold that flight theyll leave the place,
While those same hundreds mock another day
Because we have made our art of common things ...”
—William Butler Yeats (18651939)
“It is possibleindeed possible even according to the old conception of logicto give in advance a description of all true logical propositions. Hence there can never be surprises in logic.”
—Ludwig Wittgenstein (18891951)
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