Please tell me the difference between the proper subset and the power set
Answers
A subset is a collection of “some” of the elements of a set (“some” could be none or all as well). The power set is the collection of ALL subsets of a set.
Ex.
Let S = {1, 2, 3}
Here is an example of a subset of S: {2, 3}.
There is only one power set of S, and the above subset will be one of the elements of this power set.
P(S) = { { }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3} }.
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OTHER ANSWERS
Phil Scovis
Phil Scovis
Answered Jul 2, 2018 · Author has 2.3k answers and 2.2m answer views
A Power Set is the set of all subsets.
For example, the set {1,2,3}{1,2,3} has eight different subsets. {1}{1} is a subset. So is {2,3}{2,3}. So is {}{}.
However the set {1,2,3}{1,2,3} has only one power set. It is:
P({1,2,3})={{},{1},{2},{1,2},{3},{1,3},{2,3},{1,2,3}}P({1,2,3})={{},{1},{2},{1,2},{3},{1,3},{2,3},{1,2,3}}.
Sometimes, you will see things like
T∈P(S)T∈P(S)
used instead of
T⊆ST⊆S.
These really mean the same thing. In fact, this may be considered a definition of T⊆ST⊆S from more elementary concepts..
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David Townsend
David Townsend, studied at University of Warwick
Answered May 19, 2018 · Author has 8.9k answers and 1m answer views
Yes.
The power set is the set of subsets of a set S. For example, if S = {0,1}, the power set of S would be PS={ {}, {0}, {1}, {0,1} } ( where {} is the empty set). It might seem odd to talk about a set of sets, but individual sets can be members of a set too.
A subset of S would be any of the sets {}, {0}, {1}, {0,1}