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GATE 2023 ME – Question 9

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

How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6} that satisfy the condition that S is a subset of T?

  1. 729
  2. 728
  3. 665
  4. 664

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Correct answer: (A) 729

Explanation

For each of the 6 elements there are three choices: it is not in T, it is in T but not in S, or it is in both S and T. Different choices give different pairs with $S \subseteq T$, so the count is $3^6 = 729$.