If A = {2, 5, 8}, how many subsets in P(A) contain the element 5?
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Answer and explanation
Correct answer: 4
To form a subset of A that contains 5, keep 5 fixed and independently decide whether to include each of the remaining elements, 2 and 8. Each of these two elements has two choices: included or excluded. Therefore the number of suitable subsets is 2 × 2 = 2^2 = 4. They are {5}, {2, 5}, {5, 8}, and {2, 5, 8}.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
To form a subset of A that contains 5, keep 5 fixed and independently decide whether to include each of the remaining elements, 2 and 8. Each of these two elements has two choices: included or excluded. Therefore the number of suitable subsets is 2 × 2 = 2^2 = 4. They are {5}, {2, 5}, {5, 8}, and {2, 5, 8}.
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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