>[!summary] A conjunction is a tool used to connect two propositions together, the result is a new proposition that is only true if the two propositions are true. > Key equation: > Conjunctions are denoted as: $A \land B$ >[!info]+ Read Time ⏱**1 min** # Definition A conjunction is a logical tool that connects two [[Propositions |propositions]], which the result is only new proposition that is only true when **both** [[Propositions |propositions]] are **true**, otherwise returning false. [^1] If two propositions are denoted as $A$ and $B$ then the conjunction of the two is described as "A and B" or mathematically $A \land B$. A truth table for two propositions are described as the following: | $A$ | $B$ | $A \land B$ | | ----- | ----- | ----------- | | True | True | True | | True | False | False | | False | True | False | | False | False | False | --- > ✍️ This project’s been a labour of love. > If it helped, [give Math & Matter a star](https://github.com/rajeevphysics/Obsidan-MathMatter) and let me know what you'd like to see next. --- [^1]: Definition adapted from Dr. Robert Talbert lecture notes.