a set that is a part of a larger set.
Mathematics. a set consisting of elements of a given set that can be the same as the given set or smaller.

1900–05; sub- + set Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
subset (ˈsʌbˌsɛt)
1.  maths
 a.  a set the members of which are all members of some given class: A is a subset of B is usually written A⊆B
 b.  proper subset A⊂B one that is strictly contained within a larger class and excludes some of its members
2.  a set within a larger set

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

"subordinate set," 1902, from sub- + set (n.).
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Science Dictionary
subset   (sŭb'sět')  Pronunciation Key 
A set whose members are all contained in another set. The set of positive integers, for example, is a subset of the set of integers.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Example sentences
Each time a subset migrated onward, genetic diversity narrowed.
Living four-legged creatures rest and sleep in various postures, but only birds
  and a subset of mammals rest on folded limbs.
Within each of these broad questions is a subset of secondary questions waiting
  to be explored.
As it happens, only a subset of prisoners currently locked away for long
  periods of isolation would be considered truly dangerous.
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