If A = {1, 2, 3, 4, 5, 6, 7, 8}, how many subsets of the power set P(A) have at most 2 elements?
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Answer and explanation
Correct answer: 37
The set A has 8 elements. A subset with exactly r elements can be selected in C(8, r) ways. “At most 2 elements” includes subsets with 0, 1, or 2 elements. Therefore, the required number is C(8,0) + C(8,1) + C(8,2) = 1 + 8 + 28 = 37. The 0-element subset is the empty set, so it must be included.
Frequently asked questions
What is the correct answer to this question?
37
Why is this the correct answer?
The set A has 8 elements. A subset with exactly r elements can be selected in C(8, r) ways. “At most 2 elements” includes subsets with 0, 1, or 2 elements. Therefore, the required number is C(8,0) + C(8,1) + C(8,2) = 1 + 8 + 28 = 37. The 0-element subset is the empty set, so it must be included.
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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