If P(A) has 8 elements, how many non-empty subsets does A have?
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Answer and explanation
Correct answer: 7
For a set A with n elements, its power set P(A) contains 2^n elements. Since |P(A)| = 8, we have 2^n = 8 = 2^3, so |A| = 3. The power set therefore has eight total subsets, including exactly one empty set. Consequently, the number of non-empty subsets is 8 − 1 = 7, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
For a set A with n elements, its power set P(A) contains 2^n elements. Since |P(A)| = 8, we have 2^n = 8 = 2^3, so |A| = 3. The power set therefore has eight total subsets, including exactly one empty set. Consequently, the number of non-empty subsets is 8 − 1 = 7, so 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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