conjunction introduction

{{Infobox mathematical statement

| name = 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 = $\backslash frac\{P,Q\}\{\backslash therefore\; P\; \backslash land\; Q\}$

}}

{{Transformation rules}}

Conjunction introduction (often abbreviated simply as conjunction and also called and introduction or adjunction){{cite book |title=A Concise Introduction to Logic 4th edition |last=Hurley |first=Patrick |year=1991 |publisher=Wadsworth Publishing |pages=346–51 }}{{cite book |last1=Copi |first1=Irving M. |last2=Cohen |first2=Carl |last3=McMahon |first3=Kenneth |title=Introduction to Logic|date=2014 |publisher=Pearson |isbn=978-1-292-02482-0 |edition=14th|pages=370, 620}}{{cite book |last1=Moore |first1=Brooke Noel |last2=Parker |first2=Richard |title=Critical Thinking |date=2015 |publisher=McGraw Hill |location=New York |isbn=978-0-07-811914-9 |page=311 |edition=11th |chapter-url=https://archive.org/details/criticalthinking0000moor_t5e3/page/311/mode/1up |chapter-url-access=registration|chapter=Deductive Arguments II Truth-Functional Logic}} 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:

:$\backslash frac\{P,Q\}\{\backslash therefore\; P\; \backslash land\; Q\}$

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