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Set A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

nA = 10 (there are 10 entries in A)

|P(A)| = 2n

|P(A)| = 210 = 1024

P(A) represents the power set of A. The line brackets "|...|" represent the carnality (the count of elements). The power set is just a set of every possible set, including the empty set. I included this terminology to help research the topic further, if you are interested.

The answer is 1024.

Minor error in above answer: The term for the number of items in a set is its cardinality (not carnality).

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Note that an empty set is included for the set of 11 numbers. That is 1 subset. Since order doesn't matter for this type of situation, we count the following number of subsets. 1-item subset: 11 choose 1 2-item subset: 11 choose 2 3-item subset: 11 choose 3 4-item subset: 11 choose 4 5-item subset: 11 choose 5 6-item subset: 11 choose 6 7-item subset: 11 choose 7 8-item subset: 11 choose 8 9-item subset: 11 choose 9 10-item subset: 11 choose 10 11-item subset: 11 choose 11 Note that the pattern of these values follows the Fibonacci sequence. If we add all of these values and 1 altogether, then you should get 2048 subsets that belong to the given set {1,2,3,4,5,6,7,8,9,10,11}. Instead of working out with cases, you use this form, which is 2ⁿ such that n is the number of items in the set. If there is 11 items in the set, then there are 211 possible subsets!


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{1,2,4.7} is a proper subset of {1, 2, 3, 4, 4.7, 5}


Which best describes the meaning of subset?

A subset is a set where every element is also contained within another set, known as the superset. For example, if Set A contains elements {1, 2, 3}, then {1, 2} is a subset of Set A. Subsets can be proper (not equal to the superset) or improper (equal to the superset). In mathematical notation, if B is a subset of A, it is expressed as B ⊆ A.


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Related Questions

What is a subset and a proper subset?

A set is a subset of a another set if all its members are contained within the second set. A set that contains all the member of another set is still a subset of that second set.A set is a proper subset of another subset if all its members are contained within the second set and there exists at least one other member of the second set that is not in the subset.Example:For the set {1, 2, 3, 4, 5}:the set {1, 2, 3, 4, 5} is a subset set of {1, 2, 3, 4, 5}the set {1, 2, 3} is a subset of {1, 2, 3, 4, 5}, but further it is a proper subset of {1, 2, 3, 4, 5}


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What is subsets and proper subsets?

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Which best describes the meaning of subset?

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How many subsets does a set have if the set has four elements?

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How many different combinations can you make 1-10?

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