# Category:Indexed Families

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This category contains results about Indexed Families.

Definitions specific to this category can be found in Definitions/Indexed Families.

The image $\Img x$, consisting of the terms $\family {x_i}_{i \mathop \in I}$, along with the indexing function $x$ itself, is called a **family of elements of $S$ indexed by $I$**.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Indexed Families"

The following 33 pages are in this category, out of 33 total.

### D

- De Morgan's Laws (Set Theory)/Set Complement/Family of Sets/Complement of Intersection
- De Morgan's Laws (Set Theory)/Set Complement/Family of Sets/Complement of Union
- De Morgan's Laws (Set Theory)/Set Difference/Family of Sets
- De Morgan's Laws (Set Theory)/Set Difference/Family of Sets/Difference with Intersection
- De Morgan's Laws (Set Theory)/Set Difference/Family of Sets/Difference with Union

### I

- Image of Union under Relation/Family of Sets
- Indexed Cartesian Space is Set of all Mappings
- Intersection Distributes over Intersection/Families of Sets
- Intersection Distributes over Union/Family of Sets
- Intersection is Empty Implies Intersection of Subsets is Empty
- Intersection is Idempotent/Indexed Family
- Intersection is Largest Subset/Family of Sets
- Intersection is Subset/Family of Sets
- Intersection of Family is Subset of Intersection of Subset of Family

### P

### S

- Set Intersection Preserves Subsets/Families of Sets
- Set Intersection Preserves Subsets/Families of Sets/Corollary
- Set Intersection Preserves Subsets/Families of Sets/Intersection is Empty Implies Intersection of Subsets is Empty
- Set is Subset of Union/Family of Sets
- Set of Sets can be Defined as Family
- Set Union Preserves Subsets/Families of Sets

### U

- Union Distributes over Intersection/Family of Sets
- Union Distributes over Union/Families of Sets
- Union is Smallest Superset/Family of Sets
- Union of Indexed Family of Sets Equal to Union of Disjoint Sets
- Union of Inverses of Mappings is Inverse of Union of Mappings
- Union of Subset of Family is Subset of Union of Family