If |A| = 4, how many elements of P(A) have at least 3 elements?
Answer and explanation
Correct answer: 5
A subset of a four-element set can have 0, 1, 2, 3, or 4 elements. “At least 3” means exactly 3 or exactly 4 elements. The number of three-element subsets is C(4,3) = 4, because one element is omitted each time. The number of four-element subsets is C(4,4) = 1, namely A itself. Hence the required number is 4 + 1 = 5, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
A subset of a four-element set can have 0, 1, 2, 3, or 4 elements. “At least 3” means exactly 3 or exactly 4 elements. The number of three-element subsets is C(4,3) = 4, because one element is omitted each time. The number of four-element subsets is C(4,4) = 1, namely A itself. Hence the required number is 4 + 1 = 5, so 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.
