Aussagenlogik Formeln
a b f ¬∨ ¬b ¬a ¬∧ a b t
0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
vz .. -- +- .- -+ -. 00 -- ++ 00 +. +- .+ -+ ++ ..
sx .. ff fw wf .. ww ww .. fw wf ff

¬a∧¬b ¬(a∨b) ¬(¬a→b) ¬(a←¬b)
a∧¬b ¬(¬a∨b) ¬(a→b) ¬(¬a←¬b)
¬a∧b ¬(a∨¬b) ¬(¬a→¬b) ¬(a←b)
a∧b ¬(¬a∨¬b) ¬(a→¬b) ¬(¬a←b)
¬(a∧b) ¬a∨¬b a→¬b ¬a←b
¬(¬a∧b) a∨¬b ¬a→¬b a←b
¬(a∧¬b) ¬a∨b a→b ¬a←¬b
¬(¬a∧¬b) a∨b ¬a→b a←¬b
a↮b ¬a↮¬b ¬a↔b a↔¬b
a↔b ¬a↔¬b ¬a↮b a↮¬b
a↔b =
(a→b)∧(b→a) =
(a∧b)∨(¬a∧¬b)=
(¬a∨b)∧(¬b∨a)

↮b =
(a→¬b)∧(¬b→a)=
 (a∧¬b)∨(¬a∧b) =
(a∨b)∧(¬a∨¬b)

a∧b ⇒a ⇒b ⇒a∨b ⇒a↔b ⇒a→b
a∨b ⇐a ⇐b ⇐a∧b ⇐a↮b
a→b ⇐¬a ⇐b ⇐a∧b ⇐a↔b
a↔b ⇒a→b ⇒b→a
 
(a→b)∧(b→c) ⇒ ac          (a↔b)∧(b↔c) = (a→b)∧(b→c)∧(c→a)     a∧b=b∧a , a∨b=b∨a , a↔b=b↔a

a∨(b∨c) = (a∨b)∨c a∧(b∨c) = (a∧b)∨(a∧c) (a→b)∧(a→c) = a→(b∧c)
a∧(b∧c) = (a∧b)∧c a∨(b∧c) = (a∨b)∧(a∨c) (a→b)∨(a→c) = a→(b∨c)
a∨(b→c) = c∨(b→a) = b→(a∨c) a∧(b→c) = (a→b)→(a∧c) (a→c)∧(b→c) = (a∨b)→c
(a∧b)→c = a→(b→c) = ¬a∨¬b∨c (a→b)→c = (a∨c) ∧ (b→c) (a→c)∨(b→c) = (a∧b)→c
(a→b)→(a→c) = a→(b→c) a∨(b↔c) = (a∨b)↔(a∨c) a∨(b↮c) = (a∨b)↔(a←c)
(a→c)→(b→c) = c∨(b→a) a∧(b↔c) = (a∧b)↔(a→c) a∧(b↮c) = (a∧b)↮(a∧c)
(a↔b)↔c = a↔(b↔c) = (a↮b)↮c a→(b↔c) = (a∧b)↔(a∧c) a→(b↮c) = (a→b)↮(a∧c)
(a↔b)↮c = a↔(b↮c) = (a↮b)↔c a→(b↔c) = (a→b)↔(a→c) a←(b↔c) = (a∨b)↔(a←c)

(a→z)⇒(a∧b)→(z∧b) (a→z)⇒(a∨b)→(z∨b) (a→z)⇒(a→b)←(z→b) (a→z)⇒(a←b)→(z←b)
(a←z)⇒(a∧b)←(z∧b) (a←z)⇒(a∧b)←(z∧b) (a←z)⇒(a→b)→(z→b) (a←z)⇒(a←b)←(z←b)
a∧b=a∧(b∧a) a∨b=a∨(b∧¬a) a→b=a→(b∧a) a←b=a←(b∧¬a)
(a∧b)∨(c∧d) ⇒ (a∨c)∧(b∨d) (a→b)∧(c→d) ⇒ (a∧c)→(b∧d)
(a∨b)∧(c∨d) ⇐ (a∧c)∨(b∧d) (a→b)∧(c→d) ⇒ (a∨c)→(b∨d)
(a→b)∨(c→d) = (a∧c)→(b∨d)

a∧f = f (a∧b)∨a = a (a↔b)∧a = a∧b (a∧b)∨¬a =a→b (a↔b)∧¬a = ¬a∧¬b
a∧w = a (a∨b)∧a = a (a↔b)∨a = b→a (a∨b)∧¬a = ¬a∧b (a↔b)∨¬a = a→b
a∨f = a (a∧b)→a = t (a↔b)→a = a∨b (a∧b)→¬a = ¬(a∧b) (a↔b)→¬a = a→¬b
a∨w = w (a∨b)→a = b→a a→(a↔b) = a→b (a∨b)→¬a = ¬a ¬a→(a↔b) = b→a
a→f = ¬a (a→b)→a = a a↔(a∧b) = a→b (a→b)→¬a = ¬(a∧b) ¬a↔(a∧b) = ¬(a→b)
a→w = w (a→b)→b = a∨b a↔(a∨b) = b→a (a→b)→¬b = ¬b ¬a↔(a∨b) = ¬(b→a)
f→a = w a∧(a→b) = a∧b a↔(a→b) =a∧b ¬a∧(a→b) = ¬a ¬a↔(a→b) =¬(a∧b)
w→a = a a∧(b→a) = a a↔(b→a) = a∨b ¬a∧(b→a) = ¬a∧¬b ¬a↔(b→a) = (¬a∨b)
a↔w = a a∨(a→b) = t ¬a∨(a→b)  = a→b
a↔f = ¬a a∨(b→a) = b→a ¬a∨(b→a) = ¬a a∧¬a = f
a∧a = a a→(a∧b) = a→b ¬a→(a∧b) = a a∨¬a = t
a∨a = a a→(a∨b) = t ¬a→(a∨b) = a∨b a→¬a = ¬a
a→a = w a→(a→b) = a→b ¬a→(a→b) = t ¬a→a = a
a↔a = w a→(b→a) = t ¬¬a=a ¬a→(b→a) = b→a a↔¬a = f