If A = {1, 2, 3, 4, 5, 6}, how many subsets of A contain both 2 and 5?
Answer and explanation
Correct answer: 16
The elements 2 and 5 must be present in every allowed subset, so their choices are fixed. The remaining elements 1, 3, 4, and 6 are unrestricted. Each of these four elements can independently be included or excluded, giving 2⁴ possible choices. Therefore the number of subsets containing both 2 and 5 is 16, which is option B.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The elements 2 and 5 must be present in every allowed subset, so their choices are fixed. The remaining elements 1, 3, 4, and 6 are unrestricted. Each of these four elements can independently be included or excluded, giving 2⁴ possible choices. Therefore the number of subsets containing both 2 and 5 is 16, which is option B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
