Mathematical logic and foundations Definition
Biconditional
Builds on ImplicationConjunction
Definition
Let and be propositions. The biconditional of and is the proposition , read " if and only if ". The proposition is true when and are both true or both false. Otherwise, it is false.
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |
Remarks
Other notations are and " iff ". The proposition has the same truth value as .
Reading path
To understand this page from the ground up, read these 4 pages in order. The foundations come first.
Show the path as a graph
- no evidence level
- Proposition concept
- Conjunction definition
- Implication definition
- Biconditional definition
Where this leads
97 pages build on this one.
- Cantor set is closed
- Closure is closed
- Contrapositive
- Logical equivalence
- Predicate logic
- Necessary and sufficient conditions
- Propositional logic
- De Morgan's laws
- Intersection of closed sets is closed
- Proof by contrapositive
- Tautology
- A set is closed iff it equals its closure
- Zermelo–Fraenkel set theory
- Russell's paradox
- Proof by contradiction
- Double negation law
- Closure is the smallest closed superset
- Axiom of extensionality
- De Morgan's laws for sets
- Proof complexity
- Model theory
- Proof complexity
- Brouwer–Heyting–Kolmogorov interpretation
- Forcing
- Transfer principle
- Von Neumann universe
- Type theory
- Second-order logic
- Realizability
- Intuitionistic logic
- Woodin cardinal
- Naive set theory
- Many-valued logic
- Skolem's paradox
- Axiom of regularity
- Constructible universe
- Brouwer–Heyting–Kolmogorov interpretation
- Kunen's inconsistency theorem
- Interior algebra
- Borel determinacy theorem
- Singular cardinals hypothesis
- Axiom schema of replacement
- Internal set theory
- Constructive analysis
- Curry–Howard correspondence
- Cut-elimination theorem
- Ordinal analysis
- Algebraic logic
- Logical connective
- Burali-Forti paradox
- Axiom schema of replacement
- Realizability
- Cohen's independence of CH
- Homotopy type theory
- Intuitionistic type theory
- Hilbert system
- Paraconsistent logic
- Whitehead problem
- Constructivism
- Infinitary logic
- Lindström's theorem
- Theory
- Nonstandard analysis
- Modal logic
- Constructivism
- Linear logic
- Zero sharp
- Constructive analysis
- Homotopy type theory
- Set theory
- Von Neumann–Bernays–Gödel set theory
- Satisfiability
- Higher-order logic
- Intuitionistic type theory
- Logical consequence
- Lindenbaum–Tarski algebra
- Proof theory
- Axiom of regularity
- Natural deduction
- Signature
- Sequent calculus
- Axiom of constructibility
- Foundations of mathematics
- Type theory
- Gödel's consistency of CH and AC
- Jensen's covering theorem
- Set theory
- Proof theory
- Logicism
- Von Neumann–Bernays–Gödel set theory
- Church's theorem on undecidability of first-order logic
- Class
- Sequent calculus
- Axiom of determinacy
- Inner model
- Naive set theory
- Class
Further reading
- Web https://en.wikipedia.org/wiki/Logical_biconditional, lead section
About this page
| Tag | 0V6GAWTBYW |
|---|---|
| URI | m2://0V6GAWTBYW |
| Kind | definition |
| Writing | W0 stub |
| MSC | 03B05 |
| Defines | Biconditional |
| Uses | Implication, Conjunction |
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