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Question

shouldnt the answer be 1??

Comments

X = 2 ^n-1

Y = 2ⁿ

X /Y = 1/2

 ???

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ITS CORRECT 

but why X= 2^n-1

why not 2ⁿ

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Gate Fever   got it ??

Answer 1

take a small example and then analyze

1) --->when N  =  3 (Odd number)

          let S = { 1,2,3 }  --- > 8 subset possible of set S

X is subset of set of size 3 containing even number of elements

          X = { {$\Phi$ }  , {1,2} , {2,3} , {1,3}  }  = 4 subsets possible containing even number of elements

 2)  -->when N = 2 (even number)

                           S = {1,2} --- > 4 subset possible of set S

                           X = { {$\Phi$ } , {1,2} }  = 2 subsets possible  containing even number of elements

 

therefore the general formula is that if we have a sets of size = N (odd /even)

then the number of subsets with even cardinality equals the number of subsets with odd cardinality. So

this number is $\frac{1}{2}$2ⁿ=2^n−1.

 

X =  2ⁿ⁻¹

A = N elements

B  = {0 ,1 } -- > 2 elements

 

Total number of function possible from set A to set B = Y = 2ⁿ

 

$\frac{X}{Y} = \frac{2^{n-1}}{2^{n}} = \frac{1}{2}$

Comments

thanks, got it!