If A = {1, 2, 3, 4, 5, 6, 7}, how many subsets necessarily contain 2 and 5 but do not contain 7?
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Answer and explanation
Correct answer: 16
The elements 2 and 5 are compulsory, so they have no choice. Element 7 is forbidden and therefore is also fixed as absent. The remaining four elements, 1, 3, 4, and 6, can each either be included or excluded independently. Hence the number of allowed subsets is 2⁴ = 16, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The elements 2 and 5 are compulsory, so they have no choice. Element 7 is forbidden and therefore is also fixed as absent. The remaining four elements, 1, 3, 4, and 6, can each either be included or excluded independently. Hence the number of allowed subsets is 2⁴ = 16, so option C 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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