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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