If A = {1, 2, 3, 4, 5, 6, 7}, how many subsets of A contain both 3 and 7?
Answer and explanation
Correct answer: 32
The elements 3 and 7 must be included, so their choices are fixed. The other five elements, namely 1, 2, 4, 5, and 6, may independently be included or excluded. Each of these five elements gives two choices, so the number of valid subsets is 2^5 = 32. Therefore, option B is correct. The required elements do not add extra choices because they are already fixed.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The elements 3 and 7 must be included, so their choices are fixed. The other five elements, namely 1, 2, 4, 5, and 6, may independently be included or excluded. Each of these five elements gives two choices, so the number of valid subsets is 2^5 = 32. Therefore, option B is correct. The required elements do not add extra choices because they are already fixed.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
