GATE ME 2023 Set 1 — Question 9
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General Aptitude → Quantitative Aptitude → Permutations & Combinations
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Question
How many pairs of sets are possible among the subsets of that satisfy the condition that is a subset of ?
Correct answer
(A) 729
Solution
Let the universal set be with .
For any element , there are three mutually exclusive possibilities for its membership in and such that :
Since there are elements and each element has 3 independent choices, the total number of pairs is .
For , the number of pairs is .
For any element , there are three mutually exclusive possibilities for its membership in and such that :
1. and
2. and
3. and
(The case and is impossible because ).Since there are elements and each element has 3 independent choices, the total number of pairs is .
For , the number of pairs is .
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