SUBSETS Meaning and
Definition
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Subsets refer to a mathematical concept that involves a collection of elements or members that are selected from a larger set or group. In other words, a subset is a set that consists of only some of the elements present in a given set. It is denoted by the symbol ⊆.
A subset of a set A is formed by choosing any combination of elements from A, including zero elements or all the elements. For example, if set A contains the elements {1, 2, 3}, then its subsets could be {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, or {1, 2, 3}, along with the empty set {}.
It is important to note that every set is considered a subset of itself, meaning that A is a subset of A. Additionally, the empty set is considered a subset of all sets, as it contains no elements.
Subsets play a crucial role in mathematical proofs, set theory, and various other areas of mathematics. They allow for the classification and comparison of sets, categorization of elements, and the establishment of relationships between sets. Understanding subsets is integral to comprehending set operations such as union, intersection, and complement. Moreover, subsets are frequently employed to define mathematical concepts, describe properties of objects, and analyze various structures in mathematics and related fields.
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* The statistics data for these misspellings percentages are collected from over 15,411,110 spell check sessions on www.spellchecker.net from Jan 2010 - Jun 2012.
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Etymology of SUBSETS
The word "subsets" is derived from the prefix "sub-", which means "under" or "below", and the word "set", which originates from the Old English "settan" meaning "to put, place, set". In mathematics and set theory, a subset refers to a collection of elements that are part of a larger set. The term "subset" was first introduced in the mid-19th century, combining the ideas of "under" (or "below") and "set" to describe a set that is contained within another set.
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