If A = {1, 2, 3, 4} and B is a subset of A containing exactly two elements, how many such sets B are elements of the power set P(A)?
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Answer and explanation
Correct answer: 6
Every subset of A is an element of the power set P(A). To form a subset B with exactly two elements, choose any 2 elements from the 4 elements of A. The number of choices is the combination 4C2 = 4!/(2!2!) = 6. Therefore, six two-element subsets belong to P(A), so option A is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
Every subset of A is an element of the power set P(A). To form a subset B with exactly two elements, choose any 2 elements from the 4 elements of A. The number of choices is the combination 4C2 = 4!/(2!2!) = 6. Therefore, six two-element subsets belong to P(A), so option A 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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