started with 4

[mc1516.git] / e3.tex

diff --git a/e3.tex b/e3.tex
index 33bcca5..4c5e97d 100644 (file)
--- a/e3.tex
+++ b/e3.tex
@@ -37,21 +37,24 @@
                Sat(\forall(a\un \forall\ev c))=\{s_0,s_1,s_4\}\\
                \{s_0\}\subseteq \{s_0,s_1,s_4\}\text{ thus }\Phi_2\text{ is satisfied} $
        \item 
+               
        \item
                For formula:
                $$\varphi:=\al(a\ra(\neg b\un(a\wedge b)))$$
                We create an automaton $\neg\varphi$ where
-               $$\begin{array}{rl}
+               $$\begin{array}{rlr}
                        \neg\varphi 
                        & :=\ev\neg(a\ra(\neg b\un(a\wedge b)))\\
                        & :=\ev(a\wedge\neg(\neg b\un(a\wedge b)))\\
-                       & :=\ev(a\wedge(\al\neg b\vee
-                               
-                               
+                       & :=\ev(a\wedge(\al\neg b\vee(\neg b\un(a\wedge b))))\\
+                       & :=\ev(a\wedge\al\neg b)\vee\ev(a\wedge(\neg b\un(a\wedge b)))\\
+                       & :=\ev(a\wedge\neg\ev b) & \ev(a\wedge(\neg b\un(a\wedge b)))\\
                \end{array}$$
-               Elementary sets:
-               $$\begin{array}{lll}
-                       a & b & 
+               Elementary sets for $\varphi=\ev(a\wedge\neg\ev b)$ where
+               $\psi=a\wedge\neg\ev b$:
+               $$\begin{array}{llll}
+                       a & b & \varphi & \ev\psi\\
+                       a & b & \varphi & \ev\psi\\
                \end{array}$$
 \end{enumerate}
 \end{document}