If A = {1, 2, 3, 4, 5}, how many subsets in P(A) contain 2 but do not contain 5?
Answer and explanation
Correct answer: 8
The element 2 is required, so it is fixed as included. The element 5 is forbidden, so it is fixed as excluded. The remaining elements 1, 3, and 4 are unrestricted, and each has two choices: included or excluded. Consequently, the number of valid subsets is 2^3 = 8. Therefore, option B is correct; the restrictions leave three independent elements.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The element 2 is required, so it is fixed as included. The element 5 is forbidden, so it is fixed as excluded. The remaining elements 1, 3, and 4 are unrestricted, and each has two choices: included or excluded. Consequently, the number of valid subsets is 2^3 = 8. Therefore, option B is correct; the restrictions leave three independent elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
