# Exclusive Disjunction > [!NOTE] Exclusive Disjunction > The **exclusive disjunction**, **logical inequality**, **exclusive OR**, or **XOR** of a set of operands is true if an *odd number* of its operands are true. > $X\oplus Y$ > > | $X$ | $Y$ | $X\oplus Y$ | |:---:|:---:|:-----------:| | $0$ | $0$ | $0$ | | $0$ | $1$ | $1$ | | $1$ | $0$ | $1$ | | $1$ | $1$ | $0$ | > Exclusive disjunction is analogous to the [[symmetric difference]] between sets. The exclusive disjunction is effectively the [[negation]] of the [[material biconditional]]. The corresponding logic gate is the *XOR gate*. ![[XORGate.svg|200]] ## Notation In electronics the symbol for exclusive disjunction is $\oplus$. The symbol $\nleftrightarrow$ may be used in formal logic and Boolean algebra to highlight the negation of the material biconditional.