1.noun(of a set S) A set A such that every element of A is also an element of S."The set \lbrace a, b\rbrace is a both a subset and a proper subset of \lbrace a, b, c\rbrace while the set \lbrace a, b, c\rbrace is a subset of \lbrace a, b, c\rbrace but not a proper subset of \lbrace a, b, c\rbrace."