If A = {1, 2, 3, 4}, how many elements of P(A) have exactly 2 elements?
Advertisement
Answer and explanation
Correct answer: 6
Elements of P(A) are subsets of A. To form a subset with exactly two elements from the four elements 1, 2, 3, and 4, choose any two of them. The number of choices is the combination C(4,2) = 4!/(2!2!) = 6. Hence P(A) contains six two-element subsets: {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
Elements of P(A) are subsets of A. To form a subset with exactly two elements from the four elements 1, 2, 3, and 4, choose any two of them. The number of choices is the combination C(4,2) = 4!/(2!2!) = 6. Hence P(A) contains six two-element subsets: {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement