If A = {a,b,c,d}, how many members of 𝒫(A) have exactly 2 elements?
Answer and explanation
Correct answer: 6
A member of 𝒫(A) with exactly two elements is a two-element subset of the four-element set A. We must choose 2 elements from 4, and the order of selection does not matter. Therefore the number is the combination C(4,2) = 4!/(2!2!) = 6. The six subsets are {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, and {c,d}. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A member of 𝒫(A) with exactly two elements is a two-element subset of the four-element set A. We must choose 2 elements from 4, and the order of selection does not matter. Therefore the number is the combination C(4,2) = 4!/(2!2!) = 6. The six subsets are {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, and {c,d}. Hence 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.
