# File:Venn0110.svg

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

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## File history

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Date/TimeThumbnailDimensionsUserComment
current14:09, 26 July 2009384 × 280 (3 KB)Watchduck
13:28, 26 January 2008615 × 463 (4 KB)Watchduck{{Information |Description= |Source=eigene arbeit |Date= |Author= Tilman Piesk |Permission= |other_versions= }}
16:02, 22 January 2008615 × 463 (4 KB)Watchduck{{Information |Description=Venn diagrams (sometimes called Johnston diagrams) concerning propositional calculus and set theory |Source=own work |Date=2008/Jan/22 |Author=Tilman Piesk |Permission=publich domain |other_versions= }}
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