- #1
Bashyboy
- 1,421
- 5
Homework Statement
{∅,{∅}}
Homework Equations
The Attempt at a Solution
My answer is {∅, {{∅}}, {∅, {∅}}}
but the actual answer is: {∅,{∅},{{∅}},{∅,{∅}}}
I don't understand how the second element, {∅}, appears...
A power set is a set that contains all the possible subsets of a given set, including the empty set and the set itself. It is denoted by P(S) where S is the given set.
To find the power set of a given set, you can use the formula 2^n, where n is the number of elements in the given set. This means that for a set with n elements, the power set will have 2^n subsets.
The power set can be useful in many mathematical operations and proofs. It can help in determining the number of possible outcomes in a sample space, in understanding the cardinality of a set, and in proving set identities.
Yes, the power set of a given set can have an empty subset, also known as the null set. This is because the empty set is a subset of every set, including itself.
No, the power set of a given set is not always unique. This is because different sets can have the same number of elements, resulting in the same number of subsets in their power sets. However, the power set of a set is unique if and only if the set is empty or has only one element.