If A = {1, 2, 3, 4, 5, 6}, how many subsets of A contain none of the elements 1, 2, and 3?
Answer and explanation
Correct answer: 8
The condition excludes 1, 2, and 3 from every permitted subset. Thus only the remaining elements 4, 5, and 6 can be selected. Each of these three elements may independently be included or excluded, so the number of possible subsets is 2^3 = 8. The empty subset is included in this count because it contains none of the forbidden elements. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The condition excludes 1, 2, and 3 from every permitted subset. Thus only the remaining elements 4, 5, and 6 can be selected. Each of these three elements may independently be included or excluded, so the number of possible subsets is 2^3 = 8. The empty subset is included in this count because it contains none of the forbidden elements. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
