# Category:Indexed Families

This category contains results about Indexed Families.

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

The codomain $S$ consisting of the terms $\left \langle {x_i} \right \rangle_{i \mathop \in I}$, along with the indexing function $x$ itself, is called a **family of elements of $S$ indexed by $I$**.

## 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
- 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

- Preimage of Intersection under Mapping/Family of Sets
- Preimage of Intersection under Mapping/Family of Sets/Proof 1
- Preimage of Intersection under Mapping/Family of Sets/Proof 2
- Preimage of Union under Mapping/Family of Sets
- Preimage of Union under Mapping/Family of Sets/Proof 1
- Preimage of Union under Mapping/Family of Sets/Proof 2
- Projection is Surjection/Family of Sets

### 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 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