If A = {1, 2, 3, 4}, how many two-element subsets are there in P(A)?
Answer and explanation
Correct answer: 6
A two-element subset is obtained by choosing 2 different elements from the 4 elements of A. Since the order of selection does not matter, combinations are used: C(4,2) = 4!/(2!2!) = 6. Thus, P(A) contains exactly 6 subsets having two elements. The total power set has 2^4 = 16 subsets, but the question asks only for those of size two.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A two-element subset is obtained by choosing 2 different elements from the 4 elements of A. Since the order of selection does not matter, combinations are used: C(4,2) = 4!/(2!2!) = 6. Thus, P(A) contains exactly 6 subsets having two elements. The total power set has 2^4 = 16 subsets, but the question asks only for those of size two.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
