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COMEDK2017MathematicsSets and Relations

The total number of subsets of a finite set A has 56 more elements than the total number of subsets of another finite set B . What is the number of elements in the set A?

Options

  1. A5
  2. B6
  3. C7
  4. D8

Correct answer

B. 6

Step-by-step solution

Let sets A and B have m and n elements, respectively. Then, 2^ m -2^ n =56 2^ n (2^ m-n -1 )=56 array ll & 2^ n (2^ m-n -1 )=8 7 & 2^ n (2^ m-n -1 )=2³ 7 array One comparing both sides, we get array ll & 2^ n =2³ and 2^ m-n -1=7 & n=3 and 2^ m-n =8 & 2^ m-n =2³ & m-n=3 & m-3=3 & m=6 array Hence, number of the elements is set A is 6 .

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