If A = {1, 2, 3, 4, 5, 6}, how many subsets do not contain 1 but must contain 6?
Advertisement
Answer and explanation
Correct answer: 16
Element 1 is forbidden, so it has no choice and cannot be selected. Element 6 is compulsory, so it is fixed as selected. The remaining four elements, 2, 3, 4, and 5, can each be independently included or excluded. Therefore the number of subsets is 2⁴ = 16, making option B correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Element 1 is forbidden, so it has no choice and cannot be selected. Element 6 is compulsory, so it is fixed as selected. The remaining four elements, 2, 3, 4, and 5, can each be independently included or excluded. Therefore the number of subsets is 2⁴ = 16, making option B correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement