Mathematical logic and foundations Definition

Disjoint sets

Definition

Let $A$ and $B$ be sets. The sets $A$ and $B$ are disjoint when $A \cap B = \varnothing$ . A family of sets $(A_i)_{i \in I}$ is pairwise disjoint when $A_i \cap A_j = \varnothing$ for all $i, j \in I$ with $i \neq j$ .

Remarks

Example: $\{1, 2\}$ and $\{3, 4\}$ are disjoint, but $\{1, 2\}$ and $\{2, 3\}$ are not. The blocks of a partition are pairwise disjoint. For finite disjoint sets, the number of elements of $A \cup B$ is the sum of the numbers of elements of $A$ and $B$ .

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Element definition
Proposition concept
Set definition
Conjunction definition
Empty set object
Intersection definition
Disjoint sets definition

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58 pages build on this one.

Tag	`0W4RPA8QH3`
URI	`m2://0W4RPA8QH3`
Kind	definition
Writing	W1 stated
MSC	03E20
Defines	Disjoint sets
Uses	Intersection, Empty set

Disjoint sets

Definition

Remarks

Reading path

Where this leads

Further reading

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