If A = {1,2,3}, how many elements of P(A) contain 1?
Answer and explanation
Correct answer: 4
A member of P(A) is a subset of A. To count subsets that contain 1, include 1 in every subset and independently decide whether to include 2 and whether to include 3. Each of these two remaining elements has two choices, included or excluded. Therefore the number of valid subsets is 2 × 2 = 2² = 4. They are {1}, {1,2}, {1,3}, and {1,2,3}. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
A member of P(A) is a subset of A. To count subsets that contain 1, include 1 in every subset and independently decide whether to include 2 and whether to include 3. Each of these two remaining elements has two choices, included or excluded. Therefore the number of valid subsets is 2 × 2 = 2² = 4. They are {1}, {1,2}, {1,3}, and {1,2,3}. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
