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

*Posted by:*Margaret Rouse

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