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If a statement's inverse is false, then its converse is false (and vice versa). If a statement's negation is false, then the statement is true (and vice versa). If a statement (or its contrapositive) and the inverse (or the converse) are both true or both false, then it is known as a logical biconditional.
In logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. More specifically, given a conditional sentence of the form P → Q {\displaystyle P\rightarrow Q} , the inverse refers to the sentence ¬ P → ¬ Q {\displaystyle \neg P\rightarrow \neg Q} .
This marks one important difference between classical and intuitionistic negation. Algebraically, classical negation is called an involution of period two. However, in intuitionistic logic , the weaker equivalence ¬ ¬ ¬ P ≡ ¬ P {\displaystyle \neg \neg \neg P\equiv \neg P} does hold.
Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...
In linguistics, negative inversion is one of many types of subject–auxiliary inversion in English.A negation (e.g. not, no, never, nothing, etc.) or a word that implies negation (only, hardly, scarcely) or a phrase containing one of these words precedes the finite auxiliary verb necessitating that the subject and finite verb undergo inversion. [1]
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).
It is equivalent to the logical negation operator (¬) in mathematical logic. Because it has only one input, it is a unary operation and has the simplest type of truth table . It is also called the complement gate [ 2 ] because it produces the ones' complement of a binary number, swapping 0s and 1s.
De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.