If A = {1, 2, 3}, how many elements of the power set P(A) contain at least one element?
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Answer and explanation
Correct answer: 7
A has 3 elements, so its power set contains 2^3 = 8 subsets. Exactly one of these subsets is empty, namely ∅, and it does not contain at least one element. Every other subset is non-empty. Therefore, the number of subsets containing at least one element is 8 − 1 = 7. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
A has 3 elements, so its power set contains 2^3 = 8 subsets. Exactly one of these subsets is empty, namely ∅, and it does not contain at least one element. Every other subset is non-empty. Therefore, the number of subsets containing at least one element is 8 − 1 = 7. Thus option B 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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