If U = {1, 2, 3, 4, 5, 6, 7} and A = {1, 2, 3}, how many proper subsets does A' have?
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Answer and explanation
Correct answer: 15
The complement of A with respect to U is A' = {4, 5, 6, 7}, so A' has 4 elements. A set with n elements has 2^n subsets, including the set itself. Therefore, A' has 2^4 = 16 total subsets. Proper subsets exclude the set A' itself, so their number is 16 - 1 = 15. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The complement of A with respect to U is A' = {4, 5, 6, 7}, so A' has 4 elements. A set with n elements has 2^n subsets, including the set itself. Therefore, A' has 2^4 = 16 total subsets. Proper subsets exclude the set A' itself, so their number is 16 - 1 = 15. Hence 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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