Question

Write power sets of tge following set A=(a,e,i,o,u)

Answer 1

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The power set of a set is a set of all its subsets( including the empty set). The power set is written as P(S), where S is an abitrary set. Your set only has one element (which is “aeiou”), so P(S) is {} and {aeiou}. Note that the set {a,e,i,o,u} is not the same as the set {aeiou}.

The set {a,e,i,o,u} has the following subsets: {}, {a}, {e}, {i}, {o}, {u}, {a,e}, {a,i},…..{a,e,i,o,u}. It has a total of 32(2^5) subsets or a power set of 32 members.

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the power set of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory, the existence of the power set of any set is postulated by the axiom of power set. The powerset of S is variously denoted as P, , P, ℙ, ℘, or 2S.