If A = {1, 2, 3}, how many non-empty subsets are in P(A)?
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Answer and explanation
Correct answer: 7
A set with n elements has 2^n total subsets because each element can either be included or excluded. Here, |A| = 3, so P(A) has 2^3 = 8 subsets. Exactly one of them is the empty set, so the number of non-empty subsets is 8 − 1 = 7. Therefore, option B is correct; 8 counts the empty set too.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
A set with n elements has 2^n total subsets because each element can either be included or excluded. Here, |A| = 3, so P(A) has 2^3 = 8 subsets. Exactly one of them is the empty set, so the number of non-empty subsets is 8 − 1 = 7. Therefore, option B is correct; 8 counts the empty set too.
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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