If A = {1, 2, 3, 4}, how many members does the power set P(A) have, excluding A itself?
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Answer and explanation
Correct answer: 15
A set with n elements has 2^n subsets because each element has two choices: it may be included or excluded. Here |A| = 4, so P(A) contains 2^4 = 16 subsets. The set A itself is one of these subsets, so excluding A gives 16 - 1 = 15. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
A set with n elements has 2^n subsets because each element has two choices: it may be included or excluded. Here |A| = 4, so P(A) contains 2^4 = 16 subsets. The set A itself is one of these subsets, so excluding A gives 16 - 1 = 15. Therefore, 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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