diff --git a/docs/loesungen.pdf b/docs/loesungen.pdf
index fead02d..d35ea40 100644
Binary files a/docs/loesungen.pdf and b/docs/loesungen.pdf differ
diff --git a/docs/loesungen.tex b/docs/loesungen.tex
index 8d46502..d3397b6 100644
--- a/docs/loesungen.tex
+++ b/docs/loesungen.tex
@@ -4066,11 +4066,11 @@ wobei
                         &\Longleftrightarrow
                             &\exists{x\in f^{-1}(B):~}f(x)=y\\
                         &\Longleftrightarrow
-                            &\exists{x\in X:~}(x\in f^{-1}(B)\,\text{und}\,f(x)=y)\\
+                            &\exists{x:~}(x\in f^{-1}(B)\,\text{und}\,f(x)=y)\\
                         &\Longleftrightarrow
-                            &\exists{x\in X:~}(f(x)=y\,\text{und}\,x\in f^{-1}(B))\\
+                            &\exists{x:~}(x\in X\,\text{und}\,f(x)\in B\,\text{und}\,f(x)=y)\\
                         &\Longleftrightarrow
-                            &\exists{x\in X:~}(y=f(x)\,\text{und}\,f(x)\in B)\\
+                            &\exists{x\in X:~}(f(x)\in B\,\text{und}\,f(x)=y)\\
                         &\Longleftrightarrow
                             &\exists{x\in X:~}(y=f(x)\,\text{und}\,y\in B)\\
                         &\Longleftrightarrow