Question

Two finite sets have m and n element respectively. The total number of subsets of first set is 112 more than the total number of sub sets of the second set. The value of m and n respectively are 

 (a) 5, 2 (b) 4, 7 (c) 7, 4 (d) 2, 5

Answer 1

(c) 7, 4

  No. of subset of first set – No of subset of second set = 112

  ∴    2^m – 2ⁿ = 112

 ∴    2ⁿ(2^m–n – 1) = 112

  ∴      2ⁿ(2^m–n – 1) = 2⁴ × 7

   ∴ comparing n = 4

     2^m–n – 1 = 7  

  i.e.       2^m–n =8 

   hence ,m – n = 3 ,  m = n + 3 = 7

    m, n = 7, 4