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If A and B are two sets such that n A = 2 and n B = 4 , then the total number of subsets of A × B not having more than 5 elements are

Options

  1. A219
  2. B247
  3. C239
  4. D248

Correct answer

A. 219

Step-by-step solution

n A × B = n A × n B = 2 × 4 = 8 ∴ total number of subsets of A × B are 2 8 = 256 For the number of subsets not having more than 5 number of elements. The required subsets = total number of subsets - (sets having 6 elements) - (sets having 7 elements) - (sets having 8 elements) = 256 - 8 × 7 2 - 8 - 1 = 21 9

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