If A = {1, 2, 3}, how many three-element subsets are there in P(A)?
Advertisement
Answer and explanation
Correct answer: 1
A three-element subset of A must contain all three elements because A itself has exactly three elements. Therefore, the only three-element subset is {1, 2, 3}, which is A itself. Since every subset of A is an element of P(A), this one subset belongs to P(A). Hence, the number of three-element subsets is C(3,3) = 1.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
A three-element subset of A must contain all three elements because A itself has exactly three elements. Therefore, the only three-element subset is {1, 2, 3}, which is A itself. Since every subset of A is an element of P(A), this one subset belongs to P(A). Hence, the number of three-element subsets is C(3,3) = 1.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement