From 70ea33373010fd68a7ba9183fc859c7083a9d7d7 Mon Sep 17 00:00:00 2001 From: Luc Date: Wed, 22 Nov 2023 10:46:03 +0100 Subject: [PATCH] Updated syntax. --- docs/en/mathematics/logic.md | 40 ++++++++++++++++++------------------ 1 file changed, 20 insertions(+), 20 deletions(-) diff --git a/docs/en/mathematics/logic.md b/docs/en/mathematics/logic.md index 9642f65..cd4530a 100644 --- a/docs/en/mathematics/logic.md +++ b/docs/en/mathematics/logic.md @@ -1,6 +1,6 @@ # Logic -*Definition*: a statement is a sentence that is either true or false, never both. +> *Definition*: a statement is a sentence that is either true or false, never both.
@@ -12,32 +12,32 @@
-*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. - -This also works the opposite way, if $B$ then $A$ ($A \Longleftarrow B$) +> *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. +> +> 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 +> *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. -* $(A \Longleftarrow B) \land (a \implies B)$. - -: This leads to the following table. - - | $A$ | $B$ | $A \implies B$ | $A \Longleftarrow B$ | $A \iff B$| - | :---: | :---: | :------------: | :------------------: | :-------: | - | true | true | true | true | true | - | true | false | false | true | false | - | false | true | true | false | false | - | false | false | true | true | true | +| $A$ | $B$ | $A \implies B$ | $A \Longleftarrow B$ | $A \iff B$| +| :---: | :---: | :------------: | :------------------: | :-------: | +| true | true | true | true | true | +| true | false | false | true | false | +| false | true | true | false | false | +| false | false | true | true | true |
-*Definition*: suppose $P$ and $Q$ are assertions. $P$ implies $Q$ if $P \implies Q$ is true. $P$ and $Q$ are equivalent if $P$ implies $Q$ and $Q$ implies $P$. +> *Definition*: suppose $P$ and $Q$ are assertions. $P$ implies $Q$ if $P \implies Q$ is true. $P$ and $Q$ are equivalent if $P$ implies $Q$ and $Q$ implies $P$. ## Methods of proof