Question
Tue April 01, 2014

# is subsets related to supersets in any form

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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