If A = {2, 3, 5, 7, 11}, how many subsets contain 2 but do not contain 11?
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Answer and explanation
Correct answer: 8
The element 2 is compulsory, so it has only one choice: it must be included. The element 11 is forbidden, so it also has only one choice: it must be excluded. The remaining three elements, 3, 5, and 7, can each be included or excluded independently. Therefore the number of valid subsets is 2³ = 8, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The element 2 is compulsory, so it has only one choice: it must be included. The element 11 is forbidden, so it also has only one choice: it must be excluded. The remaining three elements, 3, 5, and 7, can each be included or excluded independently. Therefore the number of valid subsets is 2³ = 8, so 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.
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