Question

write the powerset of A={-1,0,1}

Answer 1

As the set has 3 elements , the total power sets will be 2^3 = 8

Powerset of { -1,0,1 } will be:

{   {} , {-1} , {0} , {1} , {-1,0} , {0,1} , {-1,1} , {-1,0,1}  }

Answer 2

The power set of A is:

P(A)={ {}, {-1}, {0}, {1}, {-1,0}, {-1,1}, {0,1}, {-1,0,1} }

• By definition, a set is said to be a well defined collection of elements or items. A power set is one that is applied on an already existing set and is said to be the group or the collection of all the subsets of the given set.
• This is derived from the number of elements present in the set. As the name suggests the number of elements of a power set is equivalent to $2^{n}$ (2 to the power n) number of elements where n represents the number of items in a given set.
• This is also given to be the cardinality of the set which is the total number of elements enclosed within the set.
• This means that the power set is the same as the cardinality. Power set is denoted by the symbol P(A) where A in this case is the given set.
• The power set is defined to have a finite set of elements in it and includes the null set (∅) as well as the set itself while obtaining the power set.

• The set A is given to be A={-1,0,1}
• It has 3 elements so hence, $n=3$.
• The total number of elements in the power set will thus be $2^{n}$$\implies 2^{3} =8$     [∵ $n=3$]
• This means that the power set will contain 8 elements in total in it.
• Now, since the power set is obtained by listing out all the possibilities or the combinations of the 3 elements it can be given as:

                              P(A)={ {}, {-1}, {0}, {1}, {-1,0}, {-1,1}, {0,1}, {-1,0,1} }

This is the power set of A. The power set does not include the repetitions in its set and the above power set consists of 8 elements as calculated, including the null or the empty set with no elements and the set A itself in it.

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