Conjunction introduction

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 is true, and the proposition is true, then the logical conjunction of the two propositions and 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:

Conjunction introduction
TypeRule of inference
FieldPropositional calculus
StatementIf the proposition is true, and the proposition is true, then the logical conjunction of the two propositions and is true.
Symbolic statement

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

Formal notation

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The conjunction introduction rule may be written in sequent notation:

 

where   and   are propositions expressed in some formal system, and   is a metalogical symbol meaning that   is a syntactic consequence if   and   are each on lines of a proof in some logical system;

References

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  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.