Mathematical logic and foundations Concept
Truth table
Summary
A truth table is a table that gives the truth value of a compound proposition for each assignment of truth values to its variables. Each row of the table is one assignment, and the last column gives the value of the compound proposition. A proposition with variables has a truth table with rows.
Remarks
The truth tables of negation, conjunction, disjunction, implication and the biconditional define these connectives. A proposition is a tautology when its column has only the value true. Two propositions are logically equivalent when their columns are the same.
Reading path
To understand this page from the ground up, read these 6 pages in order. The foundations come first.
Show the path as a graph
- no evidence level
- Proposition concept
- Conjunction definition
- Disjunction definition
- Implication definition
- Negation definition
- Truth table concept
Where this leads
42 pages build on this one.
- Cantor set is closed
- Closure is closed
- Contrapositive
- Logical equivalence
- De Morgan's laws
- Intersection of closed sets is closed
- Proof by contrapositive
- Tautology
- A set is closed iff it equals its closure
- Russell's paradox
- Proof by contradiction
- Double negation law
- Closure is the smallest closed superset
- De Morgan's laws for sets
- Proof complexity
- Brouwer–Heyting–Kolmogorov interpretation
- Type theory
- Realizability
- Naive set theory
- Constructible universe
- Brouwer–Heyting–Kolmogorov interpretation
- Constructive analysis
- Curry–Howard correspondence
- Realizability
- Homotopy type theory
- Intuitionistic type theory
- Constructivism
- Constructivism
- Zero sharp
- Constructive analysis
- Homotopy type theory
- Von Neumann–Bernays–Gödel set theory
- Intuitionistic type theory
- Axiom of constructibility
- Type theory
- Gödel's consistency of CH and AC
- Jensen's covering theorem
- Von Neumann–Bernays–Gödel set theory
- Class
- Inner model
- Naive set theory
- Class
Further reading
- Web https://en.wikipedia.org/wiki/Truth_table, lead section
About this page
| Tag | 05RSK4Q657 |
|---|---|
| URI | m2://05RSK4Q657 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 03B05 |
| Uses | Negation, Conjunction, Disjunction, Implication |
| Same as |
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What this page needs for W2
- edge defines in: at least one definition (0 of 1)
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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