Logical connective and Universal quantification

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Difference between Logical connective and Universal quantification

Logical connective vs. Universal quantification

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the value of the compound sentence produced depends only on that of the original sentences and on the meaning of the connective. In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all".

Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

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Charles Sanders Peirce

Charles Sanders Peirce ("purse"; 10 September 1839 – 19 April 1914) was an American philosopher, logician, mathematician, and scientist who is sometimes known as "the father of pragmatism".

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Converse implication

Converse implication is the converse of implication, written ←. That is to say; that for any two propositions P and Q, if Q implies P, then P is the converse implication of Q. It is written P \leftarrow Q, but may also be notated P \subset Q, or "Bpq" (in Bocheński notation).

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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).

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Exclusive or

Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).

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False (logic)

In logic, false or untrue is the state of possessing negative truth value or a nullary logical connective.

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First-order logic

First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

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Logical biconditional

In logic and mathematics, the logical biconditional (sometimes known as the material biconditional) is the logical connective of two statements asserting "P if and only if Q", where P is an antecedent and Q is a consequent.

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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.

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Logical constant

In logic, a logical constant of a language \mathcal is a symbol that has the same semantic value under every interpretation of \mathcal.

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Logical disjunction

In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true.

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Logical equivalence

In logic, statements p and q are logically equivalent if they have the same logical content.

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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.

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Material conditional

The material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→".

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Material nonimplication

Material nonimplication or abjunction (Latin ab.

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Quantifier (logic)

In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula.

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Sheffer stroke

In Boolean functions and propositional calculus, the Sheffer stroke, named after Henry M. Sheffer, written ↑, also written | (not to be confused with "||", which is often used to represent disjunction), or Dpq (in Bocheński notation), denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both".

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Symbol (formal)

A logical symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern.

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