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A is a subset of B (denoted ) and, conversely, B is a superset of A (denoted ). In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B.
Learn what subsets are and how to identify them in a set. Find out the difference between proper and improper subsets, the formula to calculate them, and the power set of a set.
- 4 min
- In set theory, a set X is defined as a subset of the other set Y, if all the elements of set X should be present in the set Y. This can be symbolic...
- The classifications of subsets are: Proper subset Improper subset
- An improper subset is defined as a subset which contains all the elements present in the other subset. But in proper subsets, if X is a subset of Y...
- Proper subset: X = {2, 5, 6} and Y = {2, 3, 5, 6} Improper Subset: X = {A, B, C, D} and Y = {A, B, C, D}
- If “n” is the number of elements of a given set, then the formulas to calculate the number of subsets and a proper subset is given by: Number of s...
Learn the meaning of subset, a mathematical term for a set that is part of another set, with examples and word history. Find out how to use subset in a sentence and see related words and games.
Set A A is a subset of set B B if every member of set A A is also a member of set B B. Symbolically, this relationship is written as A ⊆ B A ⊆ B . Sets can be related to each other in several different ways: they may not share any members in common, they may share some members in common, or they may share all members in common.
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Learn what a subset is, how to identify proper and improper subsets, and how to find the number of subsets of a set. Explore the subset symbol, the power set, and the differences between proper and improper subsets with examples and formulas.
The definition of subset relationship implies that for any set \(S\), we always have \(\emptyset\subseteq S\) and \(S\subseteq S\). The empty set is unique. The power set of a set \(S\), denoted \(\wp(S)\), contains all the subsets of \(S\).
Learn the definitions and examples of subset, strict subset, and superset in set theory. Watch a video and read comments from other learners on this topic.
- 5 min
- Sal Khan
