Browse Definitions :

subset symbol

The subset symbol indicates a specific relationship between two sets. The symbol looks like the uppercase letters U and I placed close together in a sans-serif font, and rotated 90 degrees clockwise. Subset relations form the foundation of mathematical logic, including Boolean algebra, which is important in the design of computers and signal-processing systems.

Suppose there are two sets A and B. The statement "Set A is a subset of set B" is written A B. This means that every element contained in set A is also contained in set B. Any set is, by default, a subset of itself. Also, the empty set (also called the null set) is a subset of any set.

Here are some examples of true statements using the subset symbol:

{1, 2, 3, 4, 5, ... } {0, 1, 2, 3, 4, ...}
{0, 1, 2, 3, 4, ...} {0, 1, 2, 3, 4, ...}
{0, 1, 2, 3, 4} {0, 1, 2, 3, 4, ...}
{-2, -3, 4} {-2,-2.5, -3, -3.5, -4}

The following statements, however, are not true:

{-1, 0, 1, 2, 3, ...} {0, 1, 2, 3, 4, ...}
{0, 1, 2, 3, 4, ...} {0, -1, -2, -3, -4, ...}
{-2,-2.5, -3, -3.5, -4} {-2, -3, 4}

Sets can contain things other than numbers. Examples are points on a plane, points on a spherical surface, and points in three-dimensional ( 3D ) space. Subset relationships can be expressed in terms of specialized illustrations called Venn diagrams. In the illustration below, A B, and C B. The following statements are also true: A A, B B, and C C. However, it is not true that B A, nor is it true that A C, nor is it true that B C.


Compare proper subset symbol. Also see set theory and Mathematical Symbols.

This was last updated in September 2005


  • compliance risk

    Compliance risk is an organization's potential exposure to legal penalties, financial forfeiture and material loss, resulting ...

  • information governance

    Information governance is a holistic approach to managing corporate information by implementing processes, roles, controls and ...

  • enterprise document management (EDM)

    Enterprise document management (EDM) is a strategy for overseeing an organization's paper and electronic documents so they can be...


  • principle of least privilege (POLP)

    The principle of least privilege (POLP) is a concept in computer security that limits users' access rights to only what are ...

  • biometric authentication

    Biometric authentication is a security process that relies on the unique biological characteristics of individuals to verify they...

  • denial-of-service attack

    A denial-of-service (DoS) attack is a security event that occurs when an attacker makes it impossible for legitimate users to ...



  • risk mitigation

    Risk mitigation is a strategy to prepare for and lessen the effects of threats faced by a business.

  • call tree

    A call tree is a layered hierarchical communication model that is used to notify specific individuals of an event and coordinate ...

  • Disaster Recovery as a Service (DRaaS)

    Disaster recovery as a service (DRaaS) is the replication and hosting of physical or virtual servers by a third party to provide ...


  • cloud storage

    Cloud storage is a service model in which data is transmitted and stored on remote storage systems, where it is maintained, ...

  • cloud testing

    Cloud testing is the process of using the cloud computing resources of a third-party service provider to test software ...

  • storage virtualization

    Storage virtualization is the pooling of physical storage from multiple storage devices into what appears to be a single storage ...