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GATE 2024 ME – Question 7

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?

  1. 28
  2. 27
  3. 18
  4. 19

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Correct answer: (D) 19

Explanation

Counting every ordered choice of non-empty sets with $A \subseteq B \subseteq C$ gives 37, and that number is not among the options. If C is taken to be the whole set {2, 3, 5}, the count is $3 + 9 + 7 = 19$: B of size 1 (3 ways, and then A = B), B of size 2 (3 ways, with 3 choices of A each) and B = C (7 non-empty choices of A).