If A = {1, 2, 3, 4, 5}, how many subsets in P(A) must contain 1 and must not contain 5?
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Answer and explanation
Correct answer: 8
Element 1 is compulsory, so it has only one status: it must be included. Element 5 is forbidden, so it also has only one status: it must be excluded. The remaining elements 2, 3, and 4 may each be included or excluded independently, giving 2^3 = 8 possible subsets. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Element 1 is compulsory, so it has only one status: it must be included. Element 5 is forbidden, so it also has only one status: it must be excluded. The remaining elements 2, 3, and 4 may each be included or excluded independently, giving 2^3 = 8 possible subsets. Hence 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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