Exclusive disjunction in the context of Disjunction

In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as ${\displaystyle \lor }$ and read aloud as "or". For instance, the English language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula ${\displaystyle S\lor W}$, assuming that ${\displaystyle S}$ abbreviates "it is sunny" and ${\displaystyle W}$ abbreviates "it is warm".

In classical logic, disjunction is given a truth functional semantics according to which a formula ${\displaystyle \phi \lor \psi }$ is true unless both ${\displaystyle \phi }$ and ${\displaystyle \psi }$ are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an inclusive interpretation of disjunction, in contrast with exclusive disjunction. Classical proof theoretical treatments are often given in terms of rules such as disjunction introduction and disjunction elimination. Disjunction has also been given numerous non-classical treatments, motivated by problems including Aristotle's sea battle argument, Heisenberg's uncertainty principle, as well as the numerous mismatches between classical disjunction and its nearest equivalents in natural languages.

In linguistics, a yes–no question, also known as a binary question, a polar question, or a general question, is a closed-ended question whose expected answer is one of two choices, one that provides an affirmative answer to the question versus one that provides a negative answer to the question. Typically, the choices are either "yes" or "no" in English. Yes–no questions present an exclusive disjunction, namely a pair of alternatives of which only one is a felicitous answer. In English, such questions can be formed in both positive and negative forms:

• positive yes/no question: "Will you be here tomorrow?"
• negative yes/no question: "Won't you be here tomorrow?"

Yes–no questions are in contrast with non-polar wh-questions. The latter are also called content questions, and are formed with the five Ws plus an H ("who", "what", "where", "when", "why", "how"). Rather than restricting the range of possible answers to two alternatives, content questions are compatible with a broad range of alternative answers. For example, questions beginning with "who", involve a set of several alternatives, from which one is to be drawn; in this respect, they are open-ended questions. In contrast, yes–no questions are closed-ended questions, as they only permit one of two answers, namely "yes" or "no".

The XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive or (${\displaystyle \nleftrightarrow }$) from mathematical logic; that is, a true output results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. A way to remember XOR is "must have one or the other but not both".

An XOR gate may serve as a "programmable inverter" in which one input determines whether to invert the other input, or to simply pass it along with no change. Hence it functions as a inverter (a NOT gate) which may be activated or deactivated by a switch.