File:Venn0000.svg

Summary

One of 16 Venn diagrams, representing 2-ary Boolean functions like set operations and logical connectives:

X or ¬X¬A or ¬BA or ¬B¬A or BA or B¬B¬AA xor BA xnor BAB¬A and ¬BA and ¬B¬A and BA and BX and ¬X


Operations and relations in set theory and logic

 
∅c		         
A = A
11111111
 
Ac  Bc		true
A ↔ A		 
A  B		 
A  Bc		AA
 		 
A  Bc
1110011111100111
 
A  Bc		¬A  ¬B
A → ¬B		 
A  B		A  B
A ← ¬B		 
Ac B		 
A B		A¬B
 		 
A = Bc		A¬B
 		 
A B
110101101011110101101011
 
Bc		A  ¬B
A ← B		 
A		A  B
A ↔ ¬B		 
Ac		¬A  B
A → B		 
B		 
B = ∅		AB
 		 
A = ∅c		A¬B
 		 
A = ∅		AB
 		 
B = ∅c
11000101101000111100010110100011
¬B
 		 
A  Bc		A
 		 
(A  B)c		¬A
 		 
Ac  B		B
 		Bfalse
 		Atrue
 		 
A = B		Afalse
 		Btrue
 
010010010010010010010010
A  ¬B
 		 
Ac  Bc		A  B
 		 
A  B		¬A  B
 		AB
 
1000000110000001
¬A  ¬B
 		 
∅		A  B
 		 
A = Ac
00000000
false
A ↔ ¬A		A¬A
 
These sets (statements) have complements (negations).
They are in the opposite position within this matrix.		 These relations are statements, and have negations.
They are shown in a separate matrix in the box below.


This work is ineligible for copyright and therefore in the public domain because it consists entirely of information that is common property and contains no original authorship.
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