Conjunction introduction

Rules of inference
Propositional calculus
Modus ponens (A→B, A ⊢ B) Modus tollens (A→B, ¬B ⊢ ¬A) Modus ponendo tollens (¬(A∧B), A ⊢ ¬B) Conjunction introduction (A, B ⊢ A∧B) Simplification (A∧B ⊢ A) Disjunction introduction (A ⊢ A∨B) Disjunction elimination (A∨B, A→C, B→C ⊢ C) Disjunctive syllogism (A∨B, ¬A ⊢ B) Hypothetical syllogism (A→B, B→C ⊢ A→C) Constructive dilemma (A→P, B→Q, A∨B ⊢ P∨Q) Destructive dilemma (A→P, B→Q, ¬P∨¬Q ⊢ ¬A∨¬B) Biconditional introduction (A→B, B→A ⊢ A↔B) Biconditional elimination (A↔B ⊢ A→B)
Predicate calculus
Universal generalization Universal instantiation Existential generalization Existential instantiation
v · d · e

Conjunction introduction is the inference that, if p is true, and q is true, then the conjunction p and q is true.

For example, if it's true that it's raining, and it's true that I'm inside, then it's true that "it's raining and I'm inside".

Formally:

$p\,\!$

$\frac{q\,\!\qquad\quad}{}$

$( p \wedge q )$

This logic-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Rules of inference Logic Logic stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать курсовую Conditional proof English in the Commonwealth of Nations Look at other dictionaries: Conjunction (grammar) — But redirects here. For other uses, see BUT (disambiguation). In grammar, a conjunction (abbreviated conj or cnj) is a part of speech that connects two words, sentences, phrases or clauses together. A discourse connective is a conjunction joining …   Wikipedia Logical conjunction — ∧ redirects here. For exterior product, see exterior algebra. Venn diagram of …   Wikipedia Disjunction introduction — Rules of inference Propositional calculus Modus ponens (A→B, A ⊢ B) Modus tollens (A→B, ¬B ⊢ ¬A) …   Wikipedia Boolean algebra (introduction) — Boolean algebra, developed in 1854 by George Boole in his book An Investigation of the Laws of Thought , is a variant of ordinary algebra as taught in high school. Boolean algebra differs from ordinary algebra in three ways: in the values that… …   Wikipedia Commutativity of conjunction — In logic, the commutativity of conjunction demonstrates that predicates on both sides of a logical conjunction operator are interchangeable. This logical law is a part of classical logic.[1] For any propositions H1, H2, ... Hn, and permutation… …   Wikipedia Propositional calculus — In mathematical logic, a propositional calculus or logic (also called sentential calculus or sentential logic) is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules… …   Wikipedia Outline of logic — The following outline is provided as an overview of and topical guide to logic: Logic – formal science of using reason, considered a branch of both philosophy and mathematics. Logic investigates and classifies the structure of statements and… …   Wikipedia Simplification — Rules of inference Propositional calculus Modus ponens (A→B, A ⊢ B) Modus tollens (A→B, ¬B ⊢ ¬A) …   Wikipedia List of topics in logic — This is a list of topics in logic.See also: List of mathematical logic topicsAlphabetical listAAbacus logic Abduction (logic) Abductive validation Affine logic Affirming the antecedent Affirming the consequent Antecedent Antinomy Argument form… …   Wikipedia List of rules of inference — This is a list of rules of inference, logical laws that relate to mathematical formulae.IntroductionRules of inference are syntactical transformation rules which one can use to infer a conclusion from a premise to create an argument. A set of… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”