# Category:Set Difference

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This category contains results about Set Difference.

The **(set) difference** between two sets $S$ and $T$ is written $S \setminus T$, and means the set that consists of the elements of $S$ which are not elements of $T$:

- $x \in S \setminus T \iff x \in S \land x \notin T$

## Subcategories

This category has the following 19 subcategories, out of 19 total.

### D

### E

- Examples of Set Difference (2 P)

### I

### O

### R

### S

- Set Difference is Subset (3 P)
- Set Difference with Union (2 P)

## Pages in category "Set Difference"

The following 72 pages are in this category, out of 72 total.

### C

- Cardinality of Complement
- Cardinality of Set Difference
- Cardinality of Set Difference with Subset
- Cartesian Product Distributes over Set Difference
- Class Difference with Class Difference with Subclass
- Closure of Intersection and Symmetric Difference imply Closure of Set Difference
- Closure of Union and Complement imply Closure of Set Difference

### D

### I

### P

### R

### S

- Set Difference and Intersection are Disjoint
- Set Difference and Intersection form Partition
- Set Difference and Intersection form Partition/Corollary 1
- Set Difference and Intersection form Partition/Corollary 2
- Set Difference as Intersection with Complement
- Set Difference as Intersection with Relative Complement
- Set Difference as Symmetric Difference with Intersection
- Set Difference Equals First Set iff Empty Intersection
- Set Difference Intersection with First Set is Set Difference
- Set Difference Intersection with Second Set is Empty Set
- Set Difference is Anticommutative
- Set Difference is Disjoint with Reverse
- Set Difference is not Associative
- Set Difference is Right Distributive over Set Intersection
- Set Difference is Right Distributive over Union
- Set Difference is Subset
- Set Difference is Subset of Union of Differences
- Set Difference of Cartesian Products
- Set Difference of Complements
- Set Difference of Intersection with Set is Empty Set
- Set Difference of Larger Set with Smaller is Not Empty
- Set Difference over Subset
- Set Difference Union First Set is First Set
- Set Difference Union Intersection
- Set Difference Union Second Set is Union
- Set Difference with Disjoint Set
- Set Difference with Empty Set is Self
- Set Difference with Intersection
- Set Difference with Intersection is Difference
- Set Difference with Proper Subset
- Set Difference with Proper Subset is Proper Subset
- Set Difference with Self is Empty Set
- Set Difference with Set Difference
- Set Difference with Set Difference is Union of Set Difference with Intersection
- Set Difference with Set Difference is Union of Set Difference with Intersection/Corollary
- Set Difference with Subset is Superset of Set Difference
- Set Difference with Superset is Empty Set
- Set Difference with Union
- Set Difference with Union is Set Difference
- Set Differences and Intersection form Partition of Union
- Set Intersection Distributes over Set Difference
- Sigma-Algebra Closed under Set Difference
- Subset of Set Difference iff Disjoint Set