diff --git a/logique-programmable/exercices/main.tex b/logique-programmable/exercices/main.tex
index 7694b41..26c27b7 100644
--- a/logique-programmable/exercices/main.tex
+++ b/logique-programmable/exercices/main.tex
@@ -98,7 +98,9 @@
                                    &= \overline{ac + ad} \cdot a\bar{c} + b\bar{c}\bar{d} \\
                                    &= \overline{ac} \cdot \overline{ad} \cdot a\bar{c} + b\bar{c}\bar{d} \\
                                    &= (\bar{a} + \bar{c}) \cdot (\bar{a} + \bar{d}) \cdot a\bar{c} + b\bar{c}\bar{d} \\
-                                   % TODO: finish
+                                   &= (\bar{a} + \bar{a}\bar{d} + \bar{a}\bar{c} + \bar{c}\bar{d}) \cdot a\bar{c} + b\bar{c}\bar{d} \\
+                                   &= a\bar{c}\bar{d} + b\bar{c}\bar{d} \\
+                                   &= (a + b) \cdot \bar{c}\bar{d} \\
                 \end{align*}
 
         \end{enumerate}