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44 relations: Affirming the consequent, Algebra, Antecedent (logic), Associative property, Binary operation, Bipartite graph, Causality, Closed concept, Consequent, Contraposition, Cycle (graph theory), Denying the antecedent, Determinant, Duality (mathematics), Extension (semantics), Graph theory, Group (mathematics), If and only if, Independence Day (United States), Intension, Invertible matrix, Logic, Logical conjunction, Logical consequence, Logical disjunction, Logical equivalence, Mammal, Material conditional, Material implication, Matrix (mathematics), Modus ponens, Modus tollens, Ordinary language philosophy, Playing card, Predicate (mathematical logic), Proof by contrapositive, Real number, Set (mathematics), Statement (logic), Subset, Truth table, United States, Veto, Wason selection task.
Affirming the consequent
Affirming the consequent, sometimes called converse error, fallacy of the converse or confusion of necessity and sufficiency, is a formal fallacy of inferring the converse from the original statement.
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Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
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Antecedent (logic)
An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause.
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Associative property
In mathematics, the associative property is a property of some binary operations.
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Binary operation
In mathematics, a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.
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Bipartite graph
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph.
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Causality
Causality (also referred to as causation, or cause and effect) is what connects one process (the cause) with another process or state (the effect), where the first is partly responsible for the second, and the second is partly dependent on the first.
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Closed concept
A closed concept is a concept where all the necessary and sufficient conditions required to include something within the concept can be listed.
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Consequent
A consequent is the second half of a hypothetical proposition.
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Contraposition
In logic, contraposition is an inference that says that a conditional statement is logically equivalent to its contrapositive.
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Cycle (graph theory)
In graph theory, a cycle is a path of edges and vertices wherein a vertex is reachable from itself.
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Denying the antecedent
Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement.
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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Duality (mathematics)
In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself.
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Extension (semantics)
In any of several studies that treat the use of signs—for example, in linguistics, logic, mathematics, semantics, and semiotics—the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question.
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Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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Independence Day (United States)
Independence Day, also referred to as the Fourth of July or July Fourth, is a federal holiday in the United States commemorating the adoption of the Declaration of Independence on July 4, 1776.
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Intension
In linguistics, logic, philosophy, and other fields, an intension is any property or quality connoted by a word, phrase, or another symbol.
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Invertible matrix
In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
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Logic
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 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 consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
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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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Mammal
Mammals are the vertebrates within the class Mammalia (from Latin mamma "breast"), a clade of endothermic amniotes distinguished from reptiles (including birds) by the possession of a neocortex (a region of the brain), hair, three middle ear bones, and mammary glands.
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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 implication
Material implication may refer to.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Modus ponens
In propositional logic, modus ponens (MP; also modus ponendo ponens (Latin for "mode that affirms by affirming") or implication elimination) is a rule of inference.
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Modus tollens
In propositional logic, modus tollens (MT; also modus tollendo tollens (Latin for "mode that denies by denying") or denying the consequent) is a valid argument form and a rule of inference.
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Ordinary language philosophy
Ordinary language philosophy is a philosophical methodology that sees traditional philosophical problems as rooted in misunderstandings philosophers develop by distorting or forgetting what words actually mean in everyday use.
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Playing card
A playing card is a piece of specially prepared heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic, marked with distinguishing motifs and used as one of a set for playing card games.
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Predicate (mathematical logic)
In mathematical logic, a predicate is commonly understood to be a Boolean-valued function P: X→, called the predicate on X. However, predicates have many different uses and interpretations in mathematics and logic, and their precise definition, meaning and use will vary from theory to theory.
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Proof by contrapositive
In logic, the contrapositive of a conditional statement is formed by negating both terms and reversing the direction of inference.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Statement (logic)
In logic, the term statement is variously understood to mean either: In the latter case, a statement is distinct from a sentence in that a sentence is only one formulation of a statement, whereas there may be many other formulations expressing the same statement.
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Subset
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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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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United States
The United States of America (USA), commonly known as the United States (U.S.) or America, is a federal republic composed of 50 states, a federal district, five major self-governing territories, and various possessions.
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Veto
A veto – Latin for "I forbid" – is the power (used by an officer of the state, for example) to unilaterally stop an official action, especially the enactment of legislation.
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Wason selection task
The Wason selection task (or four-card problem) is a logic puzzle devised by Peter Cathcart Wason in 1966.
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References
[1] https://en.wikipedia.org/wiki/Necessity_and_sufficiency
