If A = {1, 2, 3, 4, 5}, how many subsets in P(A) contain both 1 and 2 and do not contain 5?
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Answer and explanation
Correct answer: 4
The elements 1 and 2 are compulsory, while 5 is forbidden. Thus only 3 and 4 remain optional. Each optional element can independently be included or excluded, giving 2 choices for each and therefore 2^2 = 4 valid subsets. They are {1,2}, {1,2,3}, {1,2,4}, and {1,2,3,4}. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The elements 1 and 2 are compulsory, while 5 is forbidden. Thus only 3 and 4 remain optional. Each optional element can independently be included or excluded, giving 2 choices for each and therefore 2^2 = 4 valid subsets. They are {1,2}, {1,2,3}, {1,2,4}, and {1,2,3,4}. 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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