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  • Help me solve this - LetThe number of non-empty subsets A of S such that the product of elements in A is even is : - Sets, Relations and Functions - JEE Main

Let S= \left \{ 1,2,3,\cdots ,100 \right \}. The number of non-empty subsets A of S such that the product of elements in A is even is : 

  • Option 1)

    2^{50}\left ( 2^{50}-1 \right )

     

     

     

  • Option 2)

    2^{100}-1

  • Option 3)

    2^{50}-1

  • Option 4)

    2^{50}+1

Answers (1)

best_answer

 

Number of sub set of a set -

If a set has n elements, then it has 2n sub set.

-

Subsets = Total Subsets - Number of subsets which are odd

               = 2^{100}-2^{50}

              = 2^{50}(2^{50}-1)

      

 


Option 1)

2^{50}\left ( 2^{50}-1 \right )

 

 

 

Option 2)

2^{100}-1

Option 3)

2^{50}-1

Option 4)

2^{50}+1

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