Conjunction introduction information

Conjunction introduction
Type	Rule of inference
Field	Propositional calculus
Statement	If the proposition is true, and the proposition is true, then the logical conjunction of the two propositions and is true.
Symbolic statement

Conjunction introduction (often abbreviated simply as conjunction and also called and introduction or adjunction)^[1]^[2]^[3] is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof. It is the inference that if the proposition $P$ is true, and the proposition $Q$ is true, then the logical conjunction of the two propositions $P$ and $Q$ is true. For example, if it is true that "it is raining", and it is true that "the cat is inside", then it is true that "it is raining and the cat is inside". The rule can be stated:

{\frac {P,Q}{\therefore P\land Q}}

where the rule is that wherever an instance of " $P$ " and " $Q$ " appear on lines of a proof, a " $P\land Q$ " can be placed on a subsequent line.

^ Hurley, Patrick (1991). A Concise Introduction to Logic 4th edition. Wadsworth Publishing. pp. 346–51.
^ Copi, Irving M.; Cohen, Carl; McMahon, Kenneth (2014). Introduction to Logic (14th ed.). Pearson. pp. 370, 620. ISBN 978-1-292-02482-0.
^ Moore, Brooke Noel; Parker, Richard (2015). "Deductive Arguments II Truth-Functional Logic". Critical Thinking (11th ed.). New York: McGraw Hill. p. 311. ISBN 978-0-07-811914-9.

[1] Hurley, Patrick (1991). A Concise Introduction to Logic 4th edition. Wadsworth Publishing. pp. 346–51.

[2] Copi, Irving M.; Cohen, Carl; McMahon, Kenneth (2014). Introduction to Logic (14th ed.). Pearson. pp. 370, 620. ISBN 978-1-292-02482-0.

[3] Moore, Brooke Noel; Parker, Richard (2015). "Deductive Arguments II Truth-Functional Logic". Critical Thinking (11th ed.). New York: McGraw Hill. p. 311. ISBN 978-0-07-811914-9.

Conjunction introduction information

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Conjunction introduction

Logical conjunction

Conjunction

Conjunction elimination

List of rules of inference

Modus tollens

Disjunction introduction

Double negation

Biconditional introduction

Conditional proof

Commutative property

Modus ponens

Disjunctive syllogism

Associative property

Natural deduction

Propositional calculus

Rule of inference

Distributive property

Negation introduction

Modus ponendo tollens

Constructive dilemma

Existential quantification

Hypothetical syllogism

Destructive dilemma

French conjunctions

Hilbert system

Universal generalization

Transformation rules
Propositional calculus
Rules of inference
Implication introduction / elimination (modus ponens) Biconditional introduction / elimination Conjunction introduction / elimination Disjunction introduction / elimination Disjunctive / hypothetical syllogism Constructive / destructive dilemma Absorption / modus tollens / modus ponendo tollens Negation introduction
Rules of replacement
Associativity Commutativity Distributivity Double negation De Morgan's laws Transposition Material implication Exportation Tautology
Predicate logic
Rules of inference
Universal generalization / instantiation Existential generalization / instantiation