Difference between revisions of "Power Set"
Ramamurthy S (talk | contribs) (Created page with "A power set includes all the subsets of a given set including the empty set. A power set can be imagined as a place holder of all the subsets of a given set, or, in other word...") |
Ramamurthy S (talk | contribs) |
||
| Line 4: | Line 4: | ||
The collection of all subsets of a set A is called the power set of A. It is denoted by P(A). In P(A), every element is a set. | The collection of all subsets of a set A is called the power set of A. It is denoted by P(A). In P(A), every element is a set. | ||
In general, if A is a set with n(A) = m, then it can be shown that n [ P(A)] = 2m. | |||
Set A = {1,2,3} <math>A=\{1,2,3 \}</math> | A power set is defined as the set or group of all subsets for any given set, including the empty set, which is denoted by {}, or, ϕ. A set that has 'n' elements has 2<sup>n</sup> subsets in all. For example, let Set A = {1,2,3}, therefore, the total number of elements in the set is 3. T | ||
Set <math>A=\{1,2,3 \}</math>, number of elements in the set is 3. Therefore, there are 2<sup>3</sup> elements in the power set. Let us find the power set of set A. | |||
Subesets of set <math>A=\{\},\{1\},\{2\},\{3\},\{1,2\},\{2,3\},\{1,3\},\{1,2,3\}</math> | Subesets of set <math>A=\{\},\{1\},\{2\},\{3\},\{1,2\},\{2,3\},\{1,3\},\{1,2,3\}</math> | ||
| Line 19: | Line 20: | ||
Power set P(A) = { {}, {1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3} } | Power set P(A) = { {}, {1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3} } | ||
<nowiki>----</nowiki>INCOMPLETE-- | |||
Revision as of 09:52, 26 March 2024
A power set includes all the subsets of a given set including the empty set. A power set can be imagined as a place holder of all the subsets of a given set, or, in other words, the subsets of a set are the members or elements of a power set.
Definition
The collection of all subsets of a set A is called the power set of A. It is denoted by P(A). In P(A), every element is a set.
In general, if A is a set with n(A) = m, then it can be shown that n [ P(A)] = 2m.
A power set is defined as the set or group of all subsets for any given set, including the empty set, which is denoted by {}, or, ϕ. A set that has 'n' elements has 2n subsets in all. For example, let Set A = {1,2,3}, therefore, the total number of elements in the set is 3. T
Set , number of elements in the set is 3. Therefore, there are 23 elements in the power set. Let us find the power set of set A.
Subesets of set
Power set
Subsets of set A = {}, {1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3}
Power set P(A) = { {}, {1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3} }
----INCOMPLETE--