diff --git a/docs/en/mathematics/logic.md b/docs/en/mathematics/logic.md index 8375842..9642f65 100644 --- a/docs/en/mathematics/logic.md +++ b/docs/en/mathematics/logic.md @@ -4,14 +4,16 @@
-*Definition* **- Logical operators**: let $A$ and $B$ be assertions. -* The assertion $A$ and $B$ ($A \land B$) is true, iff both $A$ and $B$ are true. -* The assertion $A$ or $B$ ($A \lor B$) is true, iff at least one of $A$ and $B$ is true. -* The negation of $A$ ($\neg A$) is true iff $A$ is false. +> *Definition* **- Logical operators**: let $A$ and $B$ be assertions. +> +> * The assertion $A$ and $B$ ($A \land B$) is true, iff both $A$ and $B$ are true. +> * The assertion $A$ or $B$ ($A \lor B$) is true, iff at least one of $A$ and $B$ is true. +> * The negation of $A$ ($\neg A$) is true iff $A$ is false.
*Definition* **- Implies**: if $A$ and $B$ are assertions then the assertion if $A$ then $B$ ($A \implies B$) is true iff + * $A$ is true and $B$ is true, * $A$ is false and $B$ is true, * $A$ is false and $B$ is false. @@ -21,6 +23,7 @@ This also works the opposite way, if $B$ then $A$ ($A \Longleftarrow B$)
*Definition* **- If and only if**: if $A$ and $B$ are assertions then the assertion $A$ if and only if $B$ (A \iff B) is true iff + * $(A \Longleftarrow B) \land (a \implies B)$. : This leads to the following table.