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Let A = 1, 2, 3, , 12 . A set S is defined as S = (a, b) A A : a 1 . The number of elements in S is equal to :

Options

  1. A45
  2. B21
  3. C66
  4. D22

Correct answer

B. 21

Step-by-step solution

The total number of ordered pairs (a, b) such that a, b A and a We first find the number of pairs (a, b) with a (2) = 1 (3) = 2 (4) = 2 (5) = 4 (6) = 2 (7) = 6 (8) = 4 (9) = 6 (10) = 4 (11) = 10 (12) = 4 The total number of pairs with (a, b) = 1 is 1 + 2 + 2 + 4 + 2 + 6 + 4 + 6 + 4 + 10 + 4 = 45 . The set S contains pairs where (a, b) > 1 . Using the complement principle, the number of elements in S is the total number of pairs minus the number of pairs with (a, b) = 1 . n(S) = 66 - 45 = 21 . Answer: 21

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