>[!abstract] >In [[Propositional logic|propositional logic]], a logical connective is a logical constant used to connect logical formulas. Common connectives include negation, disjunction, conjunction, implication, and equivalence. In standard systems of classical logic, these connectives are interpreted as truth functions (Wikipedia, 2025). | Connective | Boolean | English | Infix | Same as | | -------------------------- | ------- | --------------------------------------- | ------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------- | | Conjunction | AND | A and B<br>(both) | $ A \land B $ | | | Material biconditional | XNOR | A if and only if B<br>(both or neither) | $ A \leftrightarrow B $ | $ (A \rightarrow B) \land (B \rightarrow A) $<br>$ (A \land B) \lor (\neg A \land \neg B) $ | | Material conditional | IMPLY | If A then B | $ A \rightarrow B $ | $ \neg(A \land \neg B) $<br>$ \neg A \lor B $ | | Non-conjunction | NAND | Not both A and B | $ A \uparrow B $ | | | Non-disjunction | NOR | Neither A nor B | $ A \downarrow B $ | $ \neg(A \lor B) $<br>$ \neg A \land \neg B $ | | Negation | NOT | Not A | $ \neg A $ | $ A \rightarrow \bot $ | | Disjunction<br>(inclusive) | OR | A and/or B | $ A \lor B $ | $ \neg((\neg A)\land(\neg B)) $<br>$ (\neg A) \rightarrow B $<br>$ (A \rightarrow B) \rightarrow B $ | | Disjunction<br>(exclusive) | XOR | Either A or B | $ A \oplus B $ | $ (A \lor B) \land \neg(A \land B) $<br>$ (A \land \neg B) \lor (\neg A \land B) $<br>$ \neg((A \land B) \lor (\neg A \land \neg B)) $ | >[!related] >- **North** (upstream): [[Propositional logic]] >- **West** (similar): [[Boolean algebra]] >- **East** (different): [[Paraconsistent logic]] >- **South** (downstream): [[Truth tables]]