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Because the logical or means a disjunction formula is true when either one or both of its parts are true, it is referred to as an inclusive disjunction. This is in contrast with an exclusive disjunction, which is true when one or the other of the arguments are true, but not both (referred to as exclusive or, or XOR).
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is odd ...
So by definition, x → y is true when x is false (relevance logic rejects this definition, by viewing an implication with a false premise as something other than either true or false). Exclusive OR (XOR) The second operation, x ⊕ y, or Jxy, is called exclusive or (often abbreviated as XOR) to distinguish it from disjunction as the inclusive ...
All other logic gates may be made from these three gates; any function in binary mathematics may be implemented with them. [3] It is sometimes called the inclusive OR gate to distinguish it from XOR, the exclusive OR gate. [4] The behavior of OR is the same as XOR except in the case of a 1 for both inputs.
In logic, two propositions and are mutually exclusive if it is not logically possible for them to be true at the same time; that is, () is a tautology. To say that more than two propositions are mutually exclusive, depending on the context, means either 1. "() () is a tautology" (it is not logically possible for more than one proposition to be true) or 2. "() is a tautology" (it is not ...
Beyond logic, the term "conjunction" also refers to similar concepts in other fields: In natural language, the denotation of expressions such as English "and"; In programming languages, the short-circuit and control structure; In set theory, intersection. In lattice theory, logical conjunction (greatest lower bound).
The principle can be viewed as an example of the sieve method extensively used in number theory and is sometimes referred to as the sieve formula. [ 4 ] As finite probabilities are computed as counts relative to the cardinality of the probability space , the formulas for the principle of inclusion–exclusion remain valid when the cardinalities ...
In logic and mathematics, inclusion is the concept that all the contents of one object are also contained within a second object. [1]For example, if m and n are two logical matrices, then