Tue April 01, 2014 By: Abhinav Sharma

is subsets related to supersets in any form

Expert Reply
Tue April 01, 2014

Yes subsets is related to supersets

If A and B are sets and every element of A is also an element of B, then:

  • A is a subset of (or is included in) B, denoted by A \subseteq B,
  • B is a superset of (or includes) A, denoted by B \supseteq A.

If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B not contained in A), then

  • A is also a proper (or strict) subset of B; this is written as A\subsetneq B.
  • B is a proper superset of A; this is written as B\supsetneq A.

For any set S, the inclusion relation ⊆ is a partial order on the set \mathcal{P}(S) of all subsets of S(the power set of S).

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