Math 2.0

Mathematical logic and foundations Definition

Tautology

Builds on Propositional logicTruth table

Definition

Let φ\varphi be a formula of propositional logic with the propositional variables p1,…,pnp_1, \dots, p_n. The formula φ\varphi is a tautology when φ\varphi is true for each of the 2n2^n assignments of truth values to p1,…,pnp_1, \dots, p_n.

Remarks

Examples are p∨¬pp \lor \neg p and p→pp \to p. A formula that is false for each assignment is a contradiction. A truth table decides in a finite number of steps whether a formula is a tautology.

Reading path

To understand this page from the ground up, read these 9 pages in order. The foundations come first.

Show the path as a graph
Proposition, concept, no evidence levelPropositionconceptConjunction, definition, no evidence levelConjunctiondefinitionDisjunction, definition, no evidence levelDisjunctiondefinitionImplication, definition, no evidence levelImplicationdefinitionNegation, definition, no evidence levelNegationdefinitionBiconditional, definition, no evidence levelBiconditionaldefinitionTruth table, concept, no evidence levelTruth tableconceptPropositional logic, concept, no evidence levelPropositional logicconceptTautology, definition, no evidence levelTautologydefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Proposition concept
  2. Conjunction definition
  3. Disjunction definition
  4. Implication definition
  5. Negation definition
  6. Biconditional definition
  7. Truth table concept
  8. Propositional logic concept
  9. Tautology definition

Where this leads

41 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Tautology_(logic), lead section
About this page
Tag0D1AHYPM8N
URIm2://0D1AHYPM8N
Kinddefinition
WritingW1 stated
MSC03B05
DefinesTautology
UsesPropositional logic, Truth table

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.

What links here

Used by