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If and only if relation
In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or bidirectional implication or biimplication
Logical_biconditional
True when either but not both inputs are true
exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR
Exclusive_or
Inference in propositional logic
Biconditional elimination is the name of two valid rules of inference of propositional logic. It allows for one to infer a conditional from a biconditional
Biconditional_elimination
Mathematical table used in logic
p → q are equivalent to ¬p ∨ q. Logical equality (also known as biconditional or exclusive nor) is an operation on two logical values, typically the values
Truth_table
Logical operator in propositional calculus
variables. It corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. It is customary practice in various applications
Logical_equality
Logical connective
statements are equal. It is paraphrased by the biconditional, a logical connective between statements. The biconditional is true in two cases, where either both
If_and_only_if
Concept in logic
Psychology portal Entailment Equisatisfiability If and only if Logical biconditional Logical equality ≡ the iff symbol (U+2261 IDENTICAL TO) ∷ the a is to
Logical_equivalence
Inference in propositional logic
conditional statements. The rule makes it possible to introduce a biconditional statement into a logical proof. If P → Q {\displaystyle P\to Q} is true, and if Q
Biconditional_introduction
List of symbols used to express logical relations
suggested set of logical symbols Logic gate § Symbols Logical connective Mathematical operators and symbols in Unicode Non-logical symbol Polish notation
List_of_logic_symbols
Mathematical logic concept
the converse) are both true or both false, then it is known as a logical biconditional. In traditional logic, contraposition is a form of immediate inference
Contraposition
Topics referred to by the same term
language Condition (disambiguation) Conditional (disambiguation) Logical biconditional Logical consequence This disambiguation page lists articles associated
Conditional_statement
Symbol connecting formulas in logic
Cpq} for implication, E p q {\displaystyle Epq} for biconditional in Łukasiewicz in 1929. Such a logical connective as converse implication " ← {\displaystyle
Logical_connective
Digital logic gate
mathematical logic, also known as the material biconditional. The two-input version implements logical equality, behaving according to the truth table
XNOR_gate
Topics referred to by the same term
EQV may refer to: Logical biconditional, a type of logical connective Logical equality, a logical operator Mercedes-Benz Concept EQV, a concept van in
EQV
Properties of mathematical relationships
value of the operation or it never makes a difference. Negation, Logical biconditional, exclusive or, tautology, and contradiction are linear functions
Linearity
Overview of and topical guide to logic
implication Converse nonimplication Exclusive or Logical NOR Logical biconditional Logical conjunction Logical disjunction Material implication Material nonimplication
Outline_of_logic
Method of deriving conclusions
from premises. They are integral parts of formal logic, serving as the logical structure of valid arguments. If an argument with true premises follows
Rule_of_inference
Property of a mathematical operation
for disambiguation. An example where this does not work is the logical biconditional ↔. It is associative; thus, A ↔ (B ↔ C) is equivalent to (A ↔ B)
Associative_property
Topics referred to by the same term
the free dictionary. XOR (exclusive or) is a logical operator whose negation is the logical biconditional. XOR may also refer to: XOR cipher, an encryption
XOR_(disambiguation)
Branch of logic
connecting propositions by logical connectives representing the truth functions of conjunction, disjunction, implication, biconditional, and negation. Some sources
Propositional_logic
completeness Logical biconditional Logical conjunction Logical disjunction Logical equality Logical implication Logical negation Logical NOR Majority
List of Boolean algebra topics
List_of_Boolean_algebra_topics
Value indicating the relation of a proposition to truth
Corresponding semantics of logical connectives are truth functions, whose values are expressed in the form of truth tables. Logical biconditional becomes the equality
Truth_value
disjunction; 7, NAND, Logical NAND (Sheffer stroke); 8, AND, Logical conjunction; 9, XNOR, If and only if, Logical biconditional; 10, q, Projection function;
List_of_rules_of_inference
Polish Dominican and philosopher (1902–1995)
time, they were raised in French culture, with emphasis being placed on logicality and rationalism. In 1907, the Bocheński family moved from Czuszów in the
Józef_Maria_Bocheński
Argument whose conclusion must be true if its premises are
of an argument can be tested, proved or disproved, and depends on its logical form. In logic, an argument is a set of related statements expressing the
Validity_(logic)
Algebraic manipulation of "true" and "false"
the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted
Boolean_algebra
Testing device for logical soundness
fragment—"everything that Bill believes"—on the righthand side of the logical biconditional. Principle of bivalence Law of excluded middle Künne, Wolfgang (2003)
T-schema
Kind of proof calculus
and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural"
Natural_deduction
Device performing a Boolean function
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output
Logic_gate
fifteenth location depicting the Exclusive or and its negation, the logical biconditional. Zellweger described the Logic Alphabet as being like a "two-dimensional
Logical_Garnet
Type of logical system
existential quantification Logical connectives: ∧ for conjunction, ∨ for disjunction, → for implication, ↔ for biconditional, ¬ for negation. Some authors
First-order_logic
Concept in mathematical logic
); material conditional ( → {\displaystyle \to } ); and possibly the biconditional ( ↔ {\displaystyle \leftrightarrow } ). Further connectives can be defined
Functional_completeness
Situation in which one cannot avoid a problem because of contradictory constraints
even a condition that is true under no circumstances; it is a "vacuous biconditional" that is ultimately meaningless. Goldstein writes: The catch is this:
Catch-22_(logic)
Topics referred to by the same term
because of the definition of the variable[clarification needed] Logical biconditional, in logic (if and only if) Modular arithmetic, a ≡ b (mod m) General
≡
Claimed as largest named number
θ ∧ ( ¬ ξ ) ) ) {\displaystyle (\neg (\theta \land (\neg \xi )))} . Biconditional: ( θ ⇔ ξ ) {\displaystyle (\theta \Leftrightarrow \xi )} as ( ¬ ( (
Rayo's_number
NIMP Material nonimplication, CNIMP Converse nonimplication, EQV Logical biconditional, Negation. Expression e = new Expression("1 --> 0"); double v =
MXparser
Impossibility for separate objects to have all their properties in common
among the logical axioms governing the notion of identity, and Rudolf Carnap defined the equals sign for identity (=) in terms of this biconditional. In a
Identity_of_indiscernibles
Propositional logic theorem
combined into a single biconditional formula: ¬ ¬ P ↔ P {\displaystyle \neg \neg P\leftrightarrow P} . Since biconditionality is an equivalence relation
Double_negation
Colloquial version of Russell's paradox
{\displaystyle a\iff \neg a} . Since the sentence is false for the biconditional, the entire universal clause is false. Since the existential clause
Barber_paradox
Rule of logical inference
of P → Q {\displaystyle P\to Q} and ¬ Q {\displaystyle \neg Q} in some logical system; or as the statement of a functional tautology or theorem of propositional
Modus_tollens
Mathematical use of "there exists"
existence of an object with a given property. It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable
Existential_quantification
Form of reasoning
October 2007). "Conditional reasoning and the Wason selection task: Biconditional interpretation instead of reasoning bias". Thinking & Reasoning. 13
Deductive_reasoning
"if and only if," denoting a biconditional logical connective indicating mutual implication. ignoratio elenchi A logical fallacy where an argument misses
Glossary_of_logic
Logic formula
three" or propositional variables such as p and q, using connectives or logical operators such as NOT, AND, OR, or IMPLIES; for example: (p AND NOT q)
Propositional_formula
Pair of logical equivalences
negated, ∧ {\displaystyle \land } is the logical conjunction operator (AND), ∨ {\displaystyle \lor } is the logical disjunction operator (OR). which can be
De_Morgan's_laws
1969 non-fiction book by G. Spencer-Brown
tautology, simply write "A = ". If one replaces '=' in R1 and R2 with the biconditional, the resulting rules hold in conventional logic. However, conventional
Laws_of_Form
Rule of logical inference
symbol meaning that Q is a syntactic consequence of P and P → Q in some logical system. In classical two-valued logic, modus ponens can be interpreted
Modus_ponens
Axiom used in set theory
equality. Despite this, the axiom is sometimes given directly as a biconditional, i.e., as ∀ x ∀ y [ ∀ z ( z ∈ x ↔ z ∈ y ) ↔ x = y ] {\displaystyle \forall
Axiom_of_extensionality
Line-by-line system for natural deduction proofs
[assumption, want P] 6 | | P [negation elimination: 5] | 7 | P iff not not P [biconditional introduction: 1 - 4, 5 - 6] The null assumption, i.e., we are proving
Fitch_notation
Logical rule of inference
derives from its being a syllogism, a three-step argument, and the use of a logical disjunction (any "or" statement.) For example, "P or Q" is a disjunction
Disjunctive_syllogism
Mathematics notation with operators preceding operands
notational systems even contrasted to Alfred Whitehead and Bertrand Russell's logical notational exposition and work in Principia Mathematica. In Łukasiewicz's
Polish_notation
Type of diagrammatic notation for logic
A Randolph diagram (R-diagram) is a simple way to visualize logical expressions and combinations of sets. Randolph diagrams were created by mathematician
Randolph_diagram
Function in logic
compound statement is constructed using individual statements connected by logical connectives; if the truth value of the compound statement is entirely determined
Truth_function
Logic puzzle by Raymond Smullyan
this result. One strategy is to use complicated logical connectives in your questions (either biconditionals or some equivalent construction). Boolos' question
The_Hardest_Logic_Puzzle_Ever
Propositional calculus in which there are more than two truth values
negation (¬), conjunction (∧), disjunction (∨), implication (→K), and biconditional (↔K) are given by: The difference between the two logics lies in how
Many-valued_logic
Inference introducing a disjunction in logical proofs
deduction system. The rule makes it possible to introduce disjunctions to logical proofs. It is the inference that if P is true, then P or Q must be true
Disjunction_introduction
Tarski biconditional provides a partial definition of the concept of truth. The concept of truth is circular because some Tarski biconditionals use an
Revision_theory
Rule of inference in propositional logic
propositional logic. The rule makes it possible to introduce a conjunction into a logical proof. It is the inference that if the proposition P {\displaystyle P}
Conjunction_introduction
Property involving two mathematical operations
and mathematical logic, where each of the logical and (denoted ∧ {\displaystyle \,\land \,} ) and the logical or (denoted ∨ {\displaystyle \,\lor \,} )
Distributive_property
Rule of replacement in propositional logic
P} or Q {\displaystyle Q} and that either form can replace the other in logical proofs. In other words, if P {\displaystyle P} is true, then Q {\displaystyle
Material implication (rule of inference)
Material_implication_(rule_of_inference)
Topics referred to by the same term
radio-based identification system for the military If and only if, a biconditional logical connective between statements, where either both statements are
IFF
Rule of replacement in propositional logic
replaced by statements having conditional consequents and vice versa in logical proofs. It is the rule that: ( ( P ∧ Q ) → R ) ⇔ ( P → ( Q → R ) ) {\displaystyle
Exportation_(logic)
Commonly used rules of replacement in propositional logic
eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are: The principle of idempotency of disjunction: P ∨ P ⇔
Tautology_(rule_of_inference)
then include the following sentences, whose main connective is the biconditional: Q x [ ¬ α ( x ) ] ↔ ¬ Q ′ x [ α ( x ) ] . {\displaystyle Qx[\lnot \alpha
Rules_of_passage
Evaluation of a function on its argument
{\displaystyle \Psi (X,Y,z)} denotes the formula on the right side of the biconditional above, for any two sets, X , Y {\displaystyle X,Y} the formula Ψ {\displaystyle
Function_application
Logical rule of inference
inference (List) Implication introduction / elimination (modus ponens) Biconditional introduction / elimination Conjunction introduction / elimination Disjunction
Negation_introduction
Mathematical invariance under transformations
symmetric logical connectives include nand (not-and, or ⊼), xor (not-biconditional, or ⊻), and nor (not-or, or ⊽). Generalizing from geometrical symmetry
Symmetry
Field of philosophical logic
deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It can be used to formalize imperative logic
Deontic_logic
Logical rule of inference
inference (List) Implication introduction / elimination (modus ponens) Biconditional introduction / elimination Conjunction introduction / elimination Disjunction
Modus_ponendo_tollens
Syllogism with conditional premise(s)
{\displaystyle B} is a syntactic consequence of A {\displaystyle A} in some logical system; and expressed as a truth-functional tautology or theorem of propositional
Hypothetical_syllogism
Family of philosophical theories
where truth is predicated of sentences on the left hand side of the biconditionals such as (T) above), then deflationism is false; on the other hand, if
Deflationary_theory_of_truth
syntactic consequence of ( P → Q ) {\displaystyle (P\rightarrow Q)} in some logical system; and expressed as a truth-functional tautology or theorem of propositional
Absorption_(logic)
System of mathematical set theory
of Bernays' axioms (intersection, complement, domain) by replacing biconditionals with implications, which means they specify only the ordered pairs or
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
Rule of inference of propositional logic
inference that allows one to eliminate a disjunctive statement from a logical proof. It is the inference that if a statement P {\displaystyle P} implies
Disjunction_elimination
logical symbols with their usual definitions; and (conjunction), or (inclusive disjunction), implies (conditional), is equivalent to (biconditional)
Glossary_of_set_theory
Lattice in universal algebra
meet), ∨, Apq, (disjunction or join), →, Cpq, (implication), ↔, Epq, (biconditional), +, Jpq (exclusive disjunction or Boolean ring addition), ↛, Lpq, (nonimplication)
Post's_lattice
Notation system for natural deductive logic
numbers to indicate antecedent dependencies of the lines of sequential logical arguments based on natural deduction inference rules. 1965: The entire
Suppes–Lemmon_notation
Inference rule in logic
Q} is also a syntactic consequence of P ∧ Q {\displaystyle P\land Q} in logical system; and expressed as truth-functional tautologies or theorems of propositional
Conjunction_elimination
Rule of inference of propositional logic
→ S {\displaystyle R\to S} , and P ∨ R {\displaystyle P\lor R} in some logical system; and expressed as a truth-functional tautology or theorem of propositional
Constructive_dilemma
Indian-American philosopher (born 1949)
theory takes truth to be a circular concept, defined by the Tarski biconditionals, 'A' is true if and only if A, and interprets it in a new way. Rather
Anil_Gupta_(philosopher)
Formal proof
C (if A, then C) from the first two premises below: Deduction theorem Logical consequence Propositional calculus Robert L. Causey, Logic, sets, and recursion
Conditional_proof
Rule of inference of propositional logic
{\displaystyle R\to S} , and ¬ Q ∨ ¬ S {\displaystyle \neg Q\lor \neg S} in some logical system; and expressed as a truth-functional tautology or theorem of propositional
Destructive_dilemma
for reasoning fallacies in children as well as adults: If is not the biconditional". Developmental Psychology. 19 (4): 471–481. doi:10.1037/0012-1649.19
Martin_Braine
LOGICAL BICONDITIONAL
LOGICAL BICONDITIONAL
Girl/Female
Tamil
Give light to others
Boy/Male
Indian, Sanskrit
Endowed with Mind; Logical
Girl/Female
Indian, Modern, Sanskrit
Magical
Boy/Male
Hindu, Indian
Logical
Girl/Female
Hindu, Indian
Give Light to Others
Girl/Female
Danish, Hindu, Indian, Japanese
Ray of Light; Logical
Boy/Male
Hindu
Love and kindness, Analytical, Logical
Girl/Female
Native American
Magical dancer.
Boy/Male
Tamil
Love and kindness, Analytical, Logical
Girl/Female
African, Arabic, French, Indian, Muslim, Swahili, Tamil
Intelligent; Logical; Intelligent One who Reasons; Wise
Girl/Female
Indian
Successful; Logical Thinkers
Boy/Male
German, Swedish
Elf; Magical Army; Warrior
Girl/Female
Australian, French, Swedish
Elf; Magical Counsel
Boy/Male
Tamil
Intelligent, Logical
Boy/Male
Gujarati, Hindu, Indian, Sanskrit
Logical Science
Boy/Male
Indian
Intelligent, Logical
Girl/Female
Hindu
Girl/Female
Indian, Tamil
King Rama's Wife
Boy/Male
Hindu, Indian
A Magical Sword
Boy/Male
Indian, Sanskrit
Logician
LOGICAL BICONDITIONAL
LOGICAL BICONDITIONAL
Girl/Female
Hindu
A celestial maiden, An Angel, Most beautiful of apsaras
Girl/Female
Muslim
The one who brings happiness
Male
Celtic
, the awe-inspiring, divine king.
Girl/Female
Tamil
Moonlight, Full Moon
Boy/Male
Arabic, Muslim, Sindhi
Resembling
Girl/Female
Arabic
Keeping Faith; Satisfying
Boy/Male
Hindu
Near, Literature
Surname or Lastname
English, Irish, and French
English, Irish, and French : from a diminutive of Noble. The Irish name is of Huguenot origin.
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Mythological, Tamil, Telugu
Goddess Parvati
Boy/Male
Hindu, Indian, Marathi, Sanskrit
Born of Wood; Fire; Happiness
LOGICAL BICONDITIONAL
LOGICAL BICONDITIONAL
LOGICAL BICONDITIONAL
LOGICAL BICONDITIONAL
LOGICAL BICONDITIONAL
a.
Skilled in logic; versed in the art of thinking and reasoning; as, he is a logical thinker.
n.
A treatise on logic; as, Mill's Logic.
a.
Having or observing logical sequence; logically consistent and rigorous; consecutive in development or transition of thought.
a.
Excessively logical; adhering too closely to the forms or rules of logic.
n.
Of or pertaining to a place; limited; logical application; as, a topical remedy; a topical claim or privilege.
a.
Exciting mirth; droll; laughable; as, a comical story.
a.
Having a mixture of seriousness and sport; serious and comical.
a.
According to the rules of logic; as, a logical argument or inference; the reasoning is logical.
n.
A logical deduction.
a.
Of or pertaining to the nodes; from a node to the same node again; as, the nodical revolutions of the moon.
v. t.
Consistent; logical.
a.
Of or pertaining to logic; used in logic; as, logical subtilties.
a.
Logical.
a.
Half logical; partly logical; said of fallacies.
adv.
In a logical manner; as, to argue logically.
a.
Having the form of, or resembling, a geometrical cone; round and tapering to a point, or gradually lessening in circumference; as, a conic or conical figure; a conical vessel.
n.
A person skilled in logic.
pl.
of Lorica
n.
See Logic.
a.
Ignorant or negligent of the rules of logic or correct reasoning; as, an illogical disputant; contrary of the rules of logic or sound reasoning; as, an illogical inference.