Checked content



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.

PD-icon.svg This file 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.
The following pages on Schools Wikipedia link to this image (list may be incomplete):


I want to learn more...

SOS Children chose the best bits of Wikipedia to help you learn. SOS Children's Villages believes education is an important part of a child's life. That's why we ensure they receive nursery care as well as high-quality primary and secondary education. When they leave school, we support the children in our care as they progress to vocational training or higher education. Why not try to find out more about sponsoring a child?