If A = {1, 2, 3}, how many non-empty elements are there in P(A)?
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Answer and explanation
Correct answer: 7
The power set of a three-element set contains 2^3 = 8 subsets. Exactly one of these subsets is empty, namely ∅. Every other subset is non-empty, so the number of non-empty elements of P(A) is 8 − 1 = 7. These include the three one-element subsets, three two-element subsets, and A itself. Therefore option C is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The power set of a three-element set contains 2^3 = 8 subsets. Exactly one of these subsets is empty, namely ∅. Every other subset is non-empty, so the number of non-empty elements of P(A) is 8 − 1 = 7. These include the three one-element subsets, three two-element subsets, and A itself. Therefore option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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