If A = {1, 2, 3, 4}, how many subsets of A contain 2 and have even size?
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Answer and explanation
Correct answer: 4
Since 2 must be included, the subset already has one element. To make its total size even, we must choose an odd number of elements from the remaining set {1, 3, 4}. We can choose one element in C(3,1)=3 ways or all three elements in C(3,3)=1 way. Thus the total is 3+1=4.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Since 2 must be included, the subset already has one element. To make its total size even, we must choose an odd number of elements from the remaining set {1, 3, 4}. We can choose one element in C(3,1)=3 ways or all three elements in C(3,3)=1 way. Thus the total is 3+1=4.
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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