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¬ ˜ ! \lnot or \neg \sim: negation: not propositional logic, Boolean algebra: The statement is true if and only if A is false. A slash placed through another operator is the same as placed in front.
For Boolean algebra, this means that the logical operation signified by "+" is not the same as the inclusive disjunction signified by "∨" but is actually equivalent to the logical inequality operator signified by "≠", or what amounts to the same thing, the exclusive disjunction signified by "XOR" or "⊕". Naturally, these variations in ...
The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), [2] and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of ...
While Elementary algebra has four operations (addition, subtraction, multiplication, and division), the Boolean algebra has only three basic operations: conjunction, disjunction, and negation, expressed with the corresponding binary operators AND and OR and the unary operator NOT (), collectively referred to as Boolean operators. [18]
If Lisa is not in Europe, then she is not in Denmark (a statement of the form ). Syntactically, (1) and (2) are derivable from each other via the rules of contraposition and double negation . Semantically, (1) and (2) are true in exactly the same models (interpretations, valuations); namely, those in which either Lisa is in Denmark is false or ...
In computer science, a relational operator is a programming language construct or operator that tests or defines some kind of relation between two entities. These include numerical equality ( e.g. , 5 = 5 ) and inequalities ( e.g. , 4 ≥ 3 ).
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
Another approach is to use with equal rights connectives of a certain convenient and functionally complete, but not minimal set. This approach requires more propositional axioms, and each equivalence between logical forms must be either an axiom or provable as a theorem. The situation, however, is more complicated in intuitionistic logic.