Conjunction introduction explained

Conjunction introduction
Type:	Rule of inference
Field:	Propositional calculus
Statement:	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.
Symbolic Statement:	(P,Q)/(\therefore P \land Q)

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:(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.

Formal notation

The conjunction introduction rule may be written in sequent notation:

P, Q \vdash P \land Q

where

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

Notes and References

1. Book: Hurley, Patrick . A Concise Introduction to Logic 4th edition . 1991 . Wadsworth Publishing . 346–51 .
2. Book: Copi . Irving M. . Cohen . Carl . McMahon . Kenneth . Introduction to Logic. 2014 . Pearson . 978-1-292-02482-0 . 14th. 370, 620.
3. Book: Moore . Brooke Noel . Parker . Richard . Critical Thinking . 2015 . McGraw Hill . New York . 978-0-07-811914-9 . 311 . 11th . https://archive.org/details/criticalthinking0000moor_t5e3/page/311/mode/1up . registration. Deductive Arguments II Truth-Functional Logic.