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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

A = A
1111 1111
Ac \scriptstyle \cup Bc
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
\scriptstyle \or ¬B
A ← B
\scriptstyle \oplus B
A ↔ ¬B
¬A \scriptstyle \or B
A → 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
\scriptstyle \cap Bc
(A \scriptstyle \Delta B)c
Ac \scriptstyle \cap 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
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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