>[!summary] The negation of a proposition is the creation of another proposition of opposite truth value >[!info]+ Read Time ⏱ **2 mins** # Definition The negation of a [[Propositions|proposition]] is another proposition with the opposite truth value. Mathematically the negation of a proposition [^1] (if the proposition is denoted as $P$) is $\neg P$ In a truth table negation can be seen as: | $P$ | $\neg P$ | | ----- | -------- | | True | False | | False | True | ## Examples A simple example of negation can be said of the statement:$\begin{array}{c}P: \text{The light is on} \\ \neg P:\text{The light is not on} \end{array}$ In logic terms: If $P$ is true then $\neg P$ is false (also true visa-versa) As a truth table, this example would look like: | $P$ | $\neg P$ | | ---- | -------- | | True | False | --- Another example well use the statements and the [[Conjunction]] statement of the following: $\begin{array}{c} P: \text{It is sunny} \\ Q : \text{Is it warm } \\ P \land Q: \text{It is sunny and warm} \end{array}$ Then the negation of the conjunction statement is the following: $\neg P\land Q: \text{It is not sunny and it is warm}$ As a truth table, this example would look like: | $P$ | $Q$ | $\neg P$ | $\neg P \land Q$ | | ----- | ----- | -------- | ---------------- | | True | True | False | False | | True | False | False | False | | False | True | True | True | | False | False | True | False | --- > 🧠 Enjoy this walkthrough? [Support Math & Matter](https://github.com/rajeevphysics/Obsidian-MathMatter) with a star and help others learn more easily. --- [^1]: Definition adapted from Dr. Robert Talbert