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A set contains (2n+1) elements. The number of subsets of this set containing more than n elements is equal to 1.2power n-1 2.2power n 3.2power n+1 4.2power 2n.

A set contains (2n+1) elements. The number of subsets of this set containing more than n elements is equal to 1.2power n-1 2.2power n 3.2power n+1 4.2power 2n.

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Grade:12

1 Answers

Arun
25750 Points
6 years ago
 
Dear Abhinav
 
Consider a subset of a set of (2n+1) elements and its complement. Exactly one of the two has more than n elements.
Since the total number of sets is 2(2n+1),
And they come in complementary pairs , exactly half i.e. 22n , have more than n elements.
 
Hence option D is correct.
 
 
Regards
Arun (askIITians forum expert)

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