# File:Venn0001.svg

## Summary

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

## Operations and relations in set theory and logic

 ∅c A = A Ac $\scriptstyle \cup$ Bc trueA ↔ A A $\scriptstyle \cup$ B A $\scriptstyle \subseteq$ Bc A$\scriptstyle \Leftrightarrow$A A $\scriptstyle \supseteq$ Bc A $\scriptstyle \cup$ Bc ¬A $\scriptstyle \or$ ¬BA → ¬B A $\scriptstyle \Delta$ B A $\scriptstyle \or$ BA ← ¬B Ac $\scriptstyle \cup$ B A $\scriptstyle \supseteq$ B A$\scriptstyle \Rightarrow$¬B A = Bc A$\scriptstyle \Leftarrow$¬B A $\scriptstyle \subseteq$ B Bc A $\scriptstyle \or$ ¬BA ← B A A $\scriptstyle \oplus$ BA ↔ ¬B Ac ¬A $\scriptstyle \or$ BA → B B B = ∅ A$\scriptstyle \Leftarrow$B A = ∅c A$\scriptstyle \Leftrightarrow$¬B A = ∅ A$\scriptstyle \Rightarrow$B B = ∅c ¬B A $\scriptstyle \cap$ Bc A (A $\scriptstyle \Delta$ B)c ¬A Ac $\scriptstyle \cap$ B B B$\scriptstyle \Leftrightarrow$false A$\scriptstyle \Leftrightarrow$true A = B A$\scriptstyle \Leftrightarrow$false B$\scriptstyle \Leftrightarrow$true A $\scriptstyle \and$ ¬B Ac $\scriptstyle \cap$ Bc A $\scriptstyle \leftrightarrow$ B A $\scriptstyle \cap$ B ¬A $\scriptstyle \and$ B A$\scriptstyle \Leftrightarrow$B ¬A $\scriptstyle \and$ ¬B ∅ A $\scriptstyle \and$ B A = Ac falseA ↔ ¬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.

 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):