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== Axiome == |
== Axiome == |
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=== Kommutativ == |
=== Kommutativ === |
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A ∧ B = B ∧ A |
A ∧ B = B ∧ A |
Revision as of 20:17, 12 November 2006
Axiome
Kommutativ
A ∧ B = B ∧ A
A ∨ B = B ∨ A
Assoziativ
(A ∧ B) ∧ C = A ∧ B ∧ C
(A ∨ B) ∨ C = A ∨ B ∨ C
Distributiv
(A ∧ B) ∨ (A ∧ C) = A ∧ (B ∨ C)
(A ∨ B) ∧ (A ∨ C) = A ∨ (B ∧ C)
Vereinfachungsregeln
A ∧ 1 = A
A ∨ 1 = 1
A ∧ 0 = 0
A ∨ 0 = A
A ∧ A = A
A ∨ A = A
¬A ∧ A = 0
¬A ∨ A = 1
A ∧ (A ∨ B) = A
A ∨ (A ∧ B = A
De Morgan Gesetze
1
Q = ( A ∧ B ) ∨ (A ∧ C) = A ∧ (B ∨ C)
2
Q = ( C ∨ B) ∧ (A ∨ C) = C ∨ (B ∧ A)
3
Y = ( A ∧ B) ∨ (C ∧ D) ∨ ( D ∧ A ) ∨ ( E ∧ C) = (A ∧ (B ∨ D)) ∨ (C ∧ (D ∨ E))
4
Z = ( A ∧ B ) ∨ ( B ∧ A) = A ∧ B
5
Y = (¬C ∨ D ∨ F) ∧ (¬C ∨ E ∨ G) = ¬C ∧ ((D ∧ F) ∧ (G ∨ E))
6
X = (( A ∧ B ) ∨ C) ∧ (( A ∨ B ) ∨ D )) = (A ∧ B) ∨ (C ∧ D)
7
X = ( C ∨ D ∨ F ) ∧ (C ∨ D ∨ G ) = (C ∨ D) ∨ (F ∧ G)
8
U = ( A ∨ B) ∧ ( A ∧ C ) = ?
9
Q = (B ∧ C) ∨ (B ∧ ¬C) = B ∧ (C ∨ ¬C) = B ∧ 0 = 0
10
Y = ( G ∨ ¬F) ∧ (G ∨ F) = G ∨ (F ∧ ¬F) = G ∨ 0 = G
Are those right? I dont think so. Please check.