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File:Venn0001.svg

Summary

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

Logical connectives Hasse diagram.svg
About this image


Operations and relations in set theory and logic

 
c
          
A = A
1111 1111
 
Ac \scriptstyle \cup Bc
true
A ↔ A
 
\scriptstyle \cup B
 
\scriptstyle \subseteq Bc
A\scriptstyle \LeftrightarrowA
 
 
\scriptstyle \supseteq Bc
1110 0111 1110 0111
 
\scriptstyle \cup Bc
¬A \scriptstyle \or ¬B
A → ¬B
 
\scriptstyle \Delta B
\scriptstyle \or B
A ← ¬B
 
Ac \scriptstyle \cup B
 
A \scriptstyle \supseteq B
A\scriptstyle \Rightarrow¬B
 
 
A = Bc
A\scriptstyle \Leftarrow¬B
 
 
A \scriptstyle \subseteq B
1101 0110 1011 1101 0110 1011
 
Bc
\scriptstyle \or ¬B
A ← B
 
A
\scriptstyle \oplus B
A ↔ ¬B
 
Ac
¬A \scriptstyle \or B
A → B
 
B
 
B =
A\scriptstyle \LeftarrowB
 
 
A = c
A\scriptstyle \Leftrightarrow¬B
 
 
A =
A\scriptstyle \RightarrowB
 
 
B = c
1100 0101 1010 0011 1100 0101 1010 0011
¬B
 
 
\scriptstyle \cap Bc
A
 
 
(A \scriptstyle \Delta B)c
¬A
 
 
Ac \scriptstyle \cap B
B
 
B\scriptstyle \Leftrightarrowfalse
 
A\scriptstyle \Leftrightarrowtrue
 
 
A = B
A\scriptstyle \Leftrightarrowfalse
 
B\scriptstyle \Leftrightarrowtrue
 
0100 1001 0010 0100 1001 0010
\scriptstyle \and ¬B
 
 
Ac \scriptstyle \cap Bc
\scriptstyle \leftrightarrow B
 
 
\scriptstyle \cap B
¬A \scriptstyle \and B
 
A\scriptstyle \LeftrightarrowB
 
1000 0001 1000 0001
¬A \scriptstyle \and ¬B
 
 
\scriptstyle \and B
 
 
A = Ac
0000 0000
false
A ↔ ¬A
A\scriptstyle \Leftrightarrow¬A
 
These sets or statements have complements
or negations. They are shown inside this matrix.
These relations are statements, and have negations.
They are shown in a seperate matrix in the box below.




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