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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 |
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| Ac Bc |
true A ↔ A |
A B |
A Bc |
AA |
A Bc |
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| A Bc |
¬A ¬B A → ¬B |
A B |
A B A ← ¬B |
Ac B |
A B |
A¬B |
A = Bc |
A¬B |
A B |
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| Bc |
A ¬B A ← B |
A |
A B A ↔ ¬B |
Ac |
¬A B A → B |
B |
B = ∅ |
AB |
A = ∅c |
A¬B |
A = ∅ |
AB |
B = ∅c | |
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| ¬B |
A Bc |
A |
(A B)c |
¬A |
Ac B |
B |
Bfalse |
Atrue |
A = B |
Afalse |
Btrue | |||
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| A ¬B |
Ac Bc |
A B |
A B |
¬A B |
AB |
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| ¬A ¬B |
∅ |
A B |
A = Ac |
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| false A ↔ ¬A |
A¬A |
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| 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. | |||||||||||||
| more relations | ||||
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This work 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. |
