Mathematical logic and foundations Definition
Conjunction
Builds on Proposition
Definition
Let and be propositions. The conjunction of and is the proposition , read " and ". The proposition is true when is true and is true. In all other cases, is false.
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Remarks
Conjunction is commutative and associative: has the same truth value as . The intersection of two sets uses conjunction: means .
Reading path
To understand this page from the ground up, read these 2 pages in order. The foundations come first.
Show the path as a graph
- no evidence level
- Proposition concept
- Conjunction definition
Where this leads
458 pages build on this one.
- Closure is the set of limits of sequences
- Finite intersection property
- Prior probability
- Compact set
- Second-countable space
- A finite group is nilpotent iff it is the product of its Sylow subgroups
- Chapman–Kolmogorov equation
- Totally disconnected space
- Urysohn's lemma
- Equivalence classes form a partition
- Isolated point
- Cantor set is closed
- Open set
- Open balls form a basis of the metric topology
- Closure is closed
- Arzelà–Ascoli theorem
- Law of total variance
- Equivalence of norms in finite dimension
- Torus
- Lebesgue number lemma
- Continuous bijection from a compact space to a Hausdorff space is a homeomorphism
- Möbius strip
- Law of total expectation
- Product topology on an arbitrary product
- Contrapositive
- Compact iff complete and totally bounded
- T1 space
- Homeomorphism
- Groups of prime order are cyclic
- Composition of continuous maps is continuous
- Truth table
- Inclusion of a subspace is continuous
- Closed subsets of compact sets are compact
- Closure in a metric space
- Heine–Cantor theorem
- Basis of a topology
- Logical equivalence
- Correspondence between equivalence relations and partitions
- Continuity at a point of a topological space
- Heine–Borel theorem
- Absolutely convergent series in a Banach space converge
- Intersection of a family of sets
- Predicate logic
- Distributive laws for sets
- Sequence spaces lp
- Topological embedding
- Order of an element divides the order of the group
- Comparison of topologies
- Riesz's lemma
- Intermediate value theorem for connected spaces
- Fixed points of a p-group action
- Necessary and sufficient conditions
- Partition of a set
- Open sets characterised by neighbourhoods
- Second Sylow theorem
- Closed sets contain their limits
- Completeness of the space of bounded continuous functions
- Groups of order p squared are abelian
- Propositional logic
- Metrizable space
- Finite intersection of open sets is open
- De Morgan's laws
- Intersection of closed sets is closed
- The number of Sylow subgroups is the index of the normaliser
- Product of compact sets is compact
- Open sets of a metric space
- Metric topology
- Baire category theorem
- Finite-dimensional normed spaces are complete
- Metrizable spaces are normal
- Normal space
- Open balls are open
- Continuity via closed sets
- Connected subsets of the real line are intervals
- Proof by contrapositive
- Banach space
- Linear maps on finite-dimensional spaces are continuous
- Interior
- Sequential compactness
- Subbasis
- Topological space
- Box topology
- Dense set
- Tautology
- A set is closed iff it equals its closure
- Baire space
- Subspace topology
- Limits are unique in Hausdorff spaces
- Connected space
- Closure
- Base rate fallacy
- Law of total probability
- Epsilon-delta continuity in metric spaces
- Continuous image of a connected set is connected
- Locally compact space
- Cantor's intersection theorem
- Bounded linear maps are continuous
- Closed subsets of complete spaces are complete
- Universal property of the quotient topology
- Meagre set
- Completion of a metric space
- Closed set
- Separable space
- The alternating group A5 is simple
- Interior is the largest open subset
- Limit point
- Intersection
- Zermelo–Fraenkel set theory
- Union of open sets is open
- Russell's paradox
- First-countable space
- Proof by contradiction
- Equivalent norms
- Regular space
- Boundary
- Abelian simple groups have prime order
- Cauchy's theorem
- Tychonoff's theorem
- Bayesian inference
- Path-connected space
- Topologist's sine curve
- Complement of an open set is closed
- Compactness and sequential compactness agree in metric spaces
- Continuous image of a compact set is compact
- Venn diagram
- Posterior probability
- Nowhere dense set
- The number of Sylow subgroups divides the index
- Universal property of the product topology
- One-point compactification
- Compact Hausdorff spaces are normal
- Equicontinuity
- Hausdorff space
- Open connected subsets of R^n are path-connected
- Compact subsets of a Hausdorff space are closed
- Double negation law
- Bayes' theorem
- Connected components are closed
- Open cover
- Closed map
- Compactness via open covers
- Metric spaces are Hausdorff
- Sup norm on bounded continuous functions
- Monty Hall problem
- Converse of Lagrange's theorem fails for the alternating group A4
- Heine–Borel theorem in finite-dimensional normed spaces
- Projections are continuous
- Interior is open
- Third Sylow theorem
- Compact space
- Frattini argument
- Connected set
- T0 space
- Compact subsets of a metric space are bounded
- Cantor set is homeomorphic to the space of binary sequences
- Image of an intersection
- Size of an orbit times the size of the stabiliser
- Continuous linear map
- Path component
- Closure is the smallest closed superset
- Open map
- Continuous map of topological spaces
- Axiom of extensionality
- Equivalent metrics
- Continuous real function on a compact set attains its bounds
- Biconditional
- Quotient topology
- First Sylow theorem
- Continuity is equivalent to sequential continuity in metric spaces
- De Morgan's laws for sets
- Compact closed unit ball implies finite dimension
- Complete subspaces are closed
- Disjoint sets
- Law of total probability for an event and its complement
- Gambler's ruin
- Circle as a quotient of the real line
- Countable intersection of dense open sets is dense
- Tietze extension theorem
- Absorbing Markov chain
- Groups of order pq
- Continuity via open sets
- Closed balls are closed
- Burnside's lemma
- Proper metric space
- Product topology
- g to the order of the group is the identity
- Path-connected spaces are connected
- Operator norm
- Relative CW complex
- Proof complexity
- Riemann domain over C^n
- VC dimension
- Univalent function
- Translation surface
- Bernstein–von Mises theorem
- Busemann G-space
- Model theory
- Stone–Weierstrass theorem
- Pettis measurability theorem
- Proof complexity
- Arakelyan's theorem
- Brouwer–Heyting–Kolmogorov interpretation
- Locally compact group
- Nonexistence of infinite-dimensional Lebesgue measure
- Köthe–Toeplitz dual
- Classification of surfaces
- Namioka--Phelps
- Lagrange's theorem
- L2 convergence of Fourier series
- Forcing
- Brouwer's characterization of the Cantor space
- Boolean model
- Convergence of the Neumann series for Volterra kernels
- Transfer principle
- Exponential of a bounded operator
- Von Neumann universe
- Kolmogorov–Arnold–Moser theorem
- Schwarz–Christoffel mapping
- Type theory
- Series in Banach spaces
- Second-order logic
- Teichmüller space
- Galois group of a prime degree polynomial with two nonreal roots
- Minkowski question-mark function
- Realizability
- Céa's lemma
- Intuitionistic logic
- Consistency of the maximum likelihood estimator
- Empirical Bayes method
- Woodin cardinal
- Pettis integral
- Strongly measurable function
- Brent's method
- Mergelyan's theorem
- Naive set theory
- CW complex
- High indices theorem
- E-infinity operad
- Hille–Yosida theorem
- Bayes factor
- Many-valued logic
- Global attractor
- Skolem's paradox
- Runge's theorem
- Bump function
- Vanishing mean oscillation
- Jacobson topology
- Spectral decomposition theorem
- Banach bundle
- Axiom of regularity
- Constructible universe
- Absolute neighborhood retract
- Lindley's paradox
- Tychonoff space
- Brouwer–Heyting–Kolmogorov interpretation
- Kunen's inconsistency theorem
- Bayes estimator
- Bisection method
- Interior algebra
- Nichols–Zoeller theorem
- Lax–Milgram theorem
- Asymptotic normality of the maximum likelihood estimator
- Borel determinacy theorem
- Neumann series
- Singular cardinals hypothesis
- Standard map
- Hall's theorem on solvable groups
- Δ-complex
- Lebesgue covering dimension
- Axiom schema of replacement
- Internal set theory
- Continuous functional calculus
- Δ-system lemma
- Constructive analysis
- Moore family
- Minimum total potential energy principle
- Continuous-time Markov chain
- Curry–Howard correspondence
- Banach limit
- Branched covering
- Semiring of sets
- Pi-system
- Cut-elimination theorem
- Carathéodory's theorem on boundary extension
- Fréchet manifold
- Parry measure
- Proof that the order of an element divides the order of the group
- Arnold's cat map
- Ordinal analysis
- Algebraic logic
- Logical connective
- Burali-Forti paradox
- Topological ring
- Suslin's problem
- Axiom schema of replacement
- Hadamard gap theorem
- Singular simplicial set
- Regular surface
- Hall subgroup
- Realizability
- Harmonic measure
- FK-space
- Cohen's independence of CH
- Anosov flow
- Bochner integral
- Homotopy type theory
- Intuitionistic type theory
- Hilbert system
- Paraconsistent logic
- Whitehead problem
- Constructivism
- Sylow theorems
- Approximation of a kernel by degenerate kernels
- Complex p-adic numbers
- Continuous function with divergent Fourier series
- Infinitary logic
- Bayes risk
- Lindström's theorem
- Theory
- Fredholm map
- Nonstandard analysis
- Frattini subgroup
- Bounded sequences ℓ∞
- Sequence space
- Proof that groups of prime order are cyclic
- Krasner's lemma
- Modal logic
- Constructivism
- Action-angle coordinates
- Reduction of a first-kind Volterra equation to the second kind
- Space of convergent sequences
- Sinai billiard
- Liouville–Neumann series
- Linear logic
- Topological field
- Dvoretzky–Rogers theorem
- Zero sharp
- Constructive analysis
- Lusternik–Schnirelmann category
- Curry–Howard correspondence
- Kronecker's approximation theorem
- Homotopy type theory
- Schauder fixed-point theorem for integral equations
- Milnor's isospectral flat tori
- Set theory
- Poincaré inequality
- Von Neumann–Bernays–Gödel set theory
- Satisfiability
- Berkovich space dynamics
- Higher-order logic
- Credible interval
- Conformal modulus
- Contraction mapping principle for integral equations
- Intuitionistic type theory
- Density of trigonometric polynomials in continuous functions
- Completion of a valued field
- Orbifold
- Ill-posedness of first-kind equations
- Logical consequence
- Spectral radius formula
- Subshift of finite type
- Torus knot
- Suslin line
- Nested intervals theorem
- Compactness of integral operators
- Lindenbaum–Tarski algebra
- Hankel operator
- Orientation of a manifold
- Galerkin method
- Compactness of families of harmonic functions
- Real projective plane
- Curtis–Hedlund–Lyndon theorem
- Proof theory
- Sunflower lemma
- Orlicz–Pettis theorem
- Axiom of regularity
- Commutative Gelfand–Naimark theorem
- Jeffreys prior
- Fourier basis of L2 of the circle
- Hyperbolic set
- Nerve of a cover
- Hilbert manifold
- Jentzsch's theorem on positive kernels
- Natural deduction
- CW approximation
- Quasisymmetric map
- Liouville–Arnold theorem
- Bayesian hierarchical model
- Signature
- Sequent calculus
- Axiom of constructibility
- Foundations of mathematics
- Type theory
- Banach–Stone theorem
- Gödel's consistency of CH and AC
- Banach–Mazur theorem
- Ring of sets
- Normal family
- Cardinal characteristics of the continuum
- Jensen's covering theorem
- Set theory
- Noncommutative geometry
- Schauder basis
- Axiom A
- Tsirelson space
- Conjugate prior
- Ladyzhenskaya–Babuška–Brezzi condition
- Singular homology
- Delta derivative on a time scale
- Resolvent as Laplace transform of a semigroup
- Extremal length
- Banach algebra
- Proof theory
- Iterated function system
- Tame Fréchet space
- Logicism
- Von Neumann–Bernays–Gödel set theory
- Basel problem via Fourier series
- Banach–Lie group
- Krull topology
- Church's theorem on undecidability of first-order logic
- Banach manifold
- BK-space
- Shrinkage estimator
- Graph embedding
- Thom–Mather stratified space
- Cantor algebra
- Convenient vector space
- Proof of Lagrange's theorem
- Class
- Sequent calculus
- Particle filter
- Cantor space
- Axiom of determinacy
- Space of null sequences
- Natural boundary
- Riemann surface
- Unique solvability of Volterra equations of the second kind
- Inner model
- Pseudo-Anosov map
- Anosov diffeomorphism
- Analytic capacity
- Mittag-Leffler's theorem
- Algorithmic randomness
- Naive set theory
- Stability conjecture
- Geometric realization
- Prime end
- Torus as a group
- Class
- Sauer–Shelah lemma
- Semi-continuity
- Automorphism group of a bounded domain is a Lie group
- Rellich–Kondrachov theorem
- Bunimovich stadium
- Maximal torus
- Faber polynomials
- Montel's theorem
Further reading
- Web https://en.wikipedia.org/wiki/Logical_conjunction, lead section
About this page
| Tag | 0M28ASWG8T |
|---|---|
| URI | m2://0M28ASWG8T |
| Kind | definition |
| Writing | W1 stated |
| MSC | 03B05 |
| Defines | Conjunction |
| Uses | Proposition |
Markdown · JSON · Edit on GitHub
What this page needs for W2
- edge instance_of in: one example (0 of 1)
- edge not_instance_of in: one non-example that fails one clause (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.