If A = {1, 2, 3, 4}, how many elements of P(A) have 3 as their maximum element?
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Answer and explanation
Correct answer: 4
For a subset of A to have maximum element 3, it must contain 3 and must not contain 4. The elements 1 and 2 may each be included or excluded independently. Thus there are 2 choices for 1 and 2 choices for 2, giving 2 × 2 = 2^2 = 4 valid subsets. These are {3}, {1,3}, {2,3}, and {1,2,3}. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For a subset of A to have maximum element 3, it must contain 3 and must not contain 4. The elements 1 and 2 may each be included or excluded independently. Thus there are 2 choices for 1 and 2 choices for 2, giving 2 × 2 = 2^2 = 4 valid subsets. These are {3}, {1,3}, {2,3}, and {1,2,3}. Therefore 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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