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Converse (logic)

In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the

If and only if

In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or

Negation

In logic, negation, also called the logical complement, is an operation that takes a proposition to another proposition "not ", written , or . It is interpreted intuitively as being true when is false

Sheffer stroke

In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not

Exclusive or

Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator J and by the in

Logical NOR

In boolean logic, logical nor or joint denial is a truth-functional operator which produces a result that is the negation of logical or. That is, a sentence of the form (p NOR q) is true precisely whe

False (logic)

In logic, false or untrue is the state of possessing negative truth value or a nullary logical connective. In a truth-functional system of propositional logic, it is one of two postulated truth values

Logical truth

Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In ot

Material nonimplication

Material nonimplication or abjunction (Latin ab = "from", junctio =–"joining") is the negation of material implication. That is to say that for any two propositions and , the material nonimplication f

Logical disjunction

In logic, disjunction is a logical connective typically notated as and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic usin

Material conditional

The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol is interpreted as material implication, a formula is true unless is tr

Logical equality

Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. It gives the functional value true if both functional

Material equivalence

No description available.

Modal operator

A modal connective (or modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general, a modal operator has the "formal" property of

Indicative conditional

In natural languages, an indicative conditional is a conditional sentence such as "If Leona is at home, she isn't in Paris", whose grammatical form restricts it to discussing what could be true. Indic

Conditioned disjunction

In logic, conditioned disjunction (sometimes called conditional disjunction) is a ternary logical connective introduced by Church. Given operands p, q, and r, which represent truth-valued propositions

Converse nonimplication

In logic, converse nonimplication is a logical connective which is the negation of converse implication (equivalently, the negation of the converse of implication).

Strict conditional

In logic, a strict conditional (symbol: , or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of c

Logical connective

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the

Logical conjunction

In logic, mathematics and linguistics, And is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true. The logical connec

Logical biconditional

In logic and mathematics, the logical biconditional, sometimes known as the material biconditional, is the logical connective used to conjoin two statements P and Q to form the statement "P if and onl

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