If A = {1, 2, 3}, how many elements of P(A) are proper subsets of A?
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Answer and explanation
Correct answer: 7
A has three elements, so its power set contains 2³ = 8 subsets in total. A proper subset is a subset that is not equal to the original set A. Every subset in P(A) is contained in A, but A itself must be excluded. Therefore, the number of proper subsets is 8 − 1 = 7.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
A has three elements, so its power set contains 2³ = 8 subsets in total. A proper subset is a subset that is not equal to the original set A. Every subset in P(A) is contained in A, but A itself must be excluded. Therefore, the number of proper subsets is 8 − 1 = 7.
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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