If A = {1, 2, 3, 4}, how many subsets with four elements does A have?
Answer and explanation
Correct answer: 1
A four-element subset of A must contain all four elements because A itself has exactly four elements. There is only one way to choose all four: {1, 2, 3, 4}, which is A itself. In standard set theory, every set is a subset of itself. Equivalently, the number of four-element subsets of a four-element set is C(4,4) = 1.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
A four-element subset of A must contain all four elements because A itself has exactly four elements. There is only one way to choose all four: {1, 2, 3, 4}, which is A itself. In standard set theory, every set is a subset of itself. Equivalently, the number of four-element subsets of a four-element set is C(4,4) = 1.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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