If A = {1,2,3,4,5}, how many subsets in P(A) contain 1 or do not contain 5?
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Answer and explanation
Correct answer: 24
There are 2^5 = 32 total subsets of A. Count the opposite of the required condition: a subset fails to contain 1 or fail to omit 5 only when it does not contain 1 and does contain 5. The remaining three elements are optional, so there are 2^3 = 8 such subsets. Hence the required count is 32 - 8 = 24, option A.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
There are 2^5 = 32 total subsets of A. Count the opposite of the required condition: a subset fails to contain 1 or fail to omit 5 only when it does not contain 1 and does contain 5. The remaining three elements are optional, so there are 2^3 = 8 such subsets. Hence the required count is 32 - 8 = 24, option A.
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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