diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index 56555f0..3e52276 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -49,9 +49,9 @@
               "type": "pdf",
               "state": {
                 "file": "Concurrent Systems/slides/class 3.pdf",
-                "page": 1,
+                "page": 5,
                 "left": -9,
-                "top": 169,
+                "top": 186,
                 "zoom": 0.6
               },
               "icon": "lucide-file-text",
diff --git a/Concurrent Systems/notes/3.md b/Concurrent Systems/notes/3.md
index 4f0d343..3802f7e 100644
--- a/Concurrent Systems/notes/3.md	
+++ b/Concurrent Systems/notes/3.md	
@@ -23,7 +23,7 @@ X.test&set() :=
 (the function is implemented in an atomic way by the hardware by suspending the interruptions!)
 ```
 
-###### How do we use it?
+###### How do we use it for MUTEX?
 ```
 lock() :=
 	wait X.test&set() = 0
@@ -44,4 +44,50 @@ X.swap(v) :=
 	tmp <- X
 	X <- v
 	return tmp
-	
\ No newline at end of file
+```
+
+###### How do we use it for MUTEX?
+```
+lock() :=
+	wait X.swap(1) = 0
+	return
+
+unlock() :=
+	X <- 0
+	return
+```
+
+#### Compare&swap
+```
+X boolean register
+
+X.compare&swap(old, new) :=
+	if X = old then
+		X <- new
+		return true
+	return false
+```
+###### How do we use it for MUTEX?
+```
+Initialize X at 0
+
+lock() :=
+	wait X.compare&swap(0, 1) = true
+	return
+
+unlock() :=
+	X <- 0
+	return
+```
+
+#### Fetch&add
+Up to now, all solutions enjoy deadlock freedom, but allow for starvation. So let's use Round Robin to promote the liveness property!
+
+Let X be an integer register; the Fetch&add primitive is implemented as follows:
+```
+X.fetch&add(v) :=
+	tmp <- X
+	X <- X+v
+	return tmp
+```
+