is subsets related to supersets in any form

Asked by Abhinav Sharma | 1st Apr, 2014, 12:26: PM

Expert Answer:

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).

Answered by  | 1st Apr, 2014, 01:21: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.