Autosave: 2022-12-17 15:30:04

Logic/Boolean_functions.md

@@ -1,19 +0,0 @@
----
-categories:
-  - Mathematics
-tags: [logic]
----
-
-# Boolean functions
-
-An example of a Boolean function:
-
-$$
-f(x,y,z) = (x \land y) \lor (\lnot(x) \land z )
-$$
-
-Here is a work through where $f(1, 0, 1)$:
-
-// Insert diagram
-
-We can compute all possible outputs of the function by constructing a truth-table with each possible variable value as the

Logic/Propositional_logic/Boolean_functions.md

@@ -0,0 +1,21 @@
+---
+categories:
+  - Mathematics
+tags: [logic]
+---
+
+# Boolean functions
+
+An example of a Boolean function:
+
+$$
+f(x,y,z) = (x \land y) \lor (\lnot(x) \land z )
+$$
+
+Here is a work through where $f(1, 0, 1)$:
+
+- The first disjunction : $ \lnot(x) \land z $ is false because $x$ is 1 and $z$ is 1
+- The second disjunction: $x \land y$ is false because $x$ is 1 and $y$ is 0
+- The overall function returns true because the main connective is disjunction and one of the disjuncts (the second) evaluates to 1. Thus the output is 1.
+
+We can compute all possible outputs of the function by constructing a truth-table with each possible variable as the truth conditions and the output of the function as the truth value: