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If and only if

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In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements. [1]

35 relations: Covariance, Domain of discourse, Euler diagram, First-order logic, Formal system, Gemination, International Phonetic Alphabet, Jan Łukasiewicz, John L. Kelley, List of mathematical jargon, Logic, Logical biconditional, Logical connective, Logical disjunction, Logical equality, Material conditional, Mathematical logic, Mathematics, Metalogic, Necessity and sufficiency, Paul Halmos, Philosophy, Phonaesthetics, Polysyllogism, Proof theory, Propositional calculus, Subset, Triple bar, Truth function, Truth table, Undergraduate Texts in Mathematics, Well-formed formula, Wolfram Alpha, XNOR gate, XOR gate.


In probability theory and statistics, covariance is a measure of the joint variability of two random variables.

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Domain of discourse

In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.

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Euler diagram

Euler diagram is a diagrammatic means of representing sets and their relationships.

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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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Formal system

A formal system is the name of a logic system usually defined in the mathematical way.

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Gemination, or consonant elongation, is the pronouncing in phonetics of a spoken consonant for an audibly longer period of time than that of a short consonant.

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International Phonetic Alphabet

The International Phonetic Alphabet (IPA) is an alphabetic system of phonetic notation based primarily on the Latin alphabet.

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Jan Łukasiewicz

Jan Łukasiewicz (21 December 1878 – 13 February 1956) was a Polish logician and philosopher born in Lwów, a city in the Galician kingdom of Austria-Hungary.

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John L. Kelley

John L. Kelley (December 6, 1916, Kansas – November 26, 1999, Berkeley, California) was an American mathematician at University of California, Berkeley who worked in general topology and functional analysis.

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List of mathematical jargon

The language of mathematics has a vast vocabulary of specialist and technical terms.

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Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

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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 connective

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.

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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 equality

Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus.

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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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Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.

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Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Metalogic is the study of the metatheory of logic.

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Necessity and sufficiency

In logic, necessity and sufficiency are terms used to describe an implicational relationship between statements.

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Paul Halmos

Paul Richard Halmos (Halmos Pál; March 3, 1916 – October 2, 2006) was a Hungarian-Jewish-born American mathematician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces).

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Philosophy (from Greek φιλοσοφία, philosophia, literally "love of wisdom") is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language.

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Phonaesthetics (from the φωνή phōnē, "voice-sound"; and αἰσθητική aisthētikē, "aesthetics") is a branch of phonetics concerned with "the possible connection between sound sequences and meaning", according to Raymond Hickey.

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A polysyllogism (also called multi-premise syllogism, sorites, climax, or gradatio) is a string of any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on.

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Proof theory

Proof theory is a major branchAccording to Wang (1981), pp.

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Propositional calculus

Propositional calculus is a branch of logic.

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In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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Triple bar

The triple bar, ≡, is a symbol with multiple, context-dependent meanings.

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Truth function

In logic, a truth function is a function that accepts truth values as input and produces a truth value as output, i.e., the input and output are all truth values.

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Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001).

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Undergraduate Texts in Mathematics

Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag.

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Well-formed formula

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.

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Wolfram Alpha

Wolfram Alpha (also styled WolframAlpha, and Wolfram|Alpha) is a computational knowledge engine or answer engine developed by Wolfram Alpha LLC, a subsidiary of Wolfram Research.

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XNOR gate

The XNOR gate (often written Exclusive-NOR, sometimes: EXNOR, ENOR, NXOR, XAND) is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate.

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XOR gate

The XOR gate (sometimes EOR gate, or EXOR gate and pronounced as Exclusive OR gate) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd.

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[1] https://en.wikipedia.org/wiki/If_and_only_if

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