If A = {p, q, r}, how many two-element subsets are members of the power set P(A)?
Answer and explanation
Correct answer: 3
The set A has 3 distinct elements. A two-element subset is formed by choosing any 2 of these 3 elements, so the required number is C(3, 2) = 3!/(2!1!) = 3. Explicitly, the subsets are {p, q}, {p, r}, and {q, r}. Each of these is a member of P(A), because the power set contains every subset of A. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The set A has 3 distinct elements. A two-element subset is formed by choosing any 2 of these 3 elements, so the required number is C(3, 2) = 3!/(2!1!) = 3. Explicitly, the subsets are {p, q}, {p, r}, and {q, r}. Each of these is a member of P(A), because the power set contains every subset of A. Therefore, 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.
