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Venn Diagram Identities

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Two sets A and B with nothing in common.

$A \cap B = \varnothing$

Elements that are in set A or in set B but not in both.

$A \triangle B = (A \cup B) - (A \cap B)$

All elements that belong to set A and also belong to set B, inclusively.

$A \cup B$

Only the elements that set A and set B both have.

$A \cap B$

All elements not in set A.

$A^{c}$ or $\sim A$

Elements either in set A or set B, but not in both.

$A \oplus B$

All elements that are in the universal set but not in A or B.

$(A \cup B)^c$ or $\sim(A \cup B)$

Elements that are in set A, excluding any elements that are also in set B.

$A - B$ or $A \setminus B$

Elements in the universal set that are not in both A and B simultaneously.

$(A \cap B)^c$ or $\sim(A \cap B)$

All the possible elements that are either part of set A or everything except set B.

$A \cup B^{c}$

The scenario where neither set A nor set B has any elements.

$A = B = \varnothing$

Intersection of the complements of sets A and B.

$A^{c} \cap B^{c}$

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