# Category: Logical connectives

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