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GATE 2021 CS (CS2) – Question 60

Engineering Mathematics · Discrete Mathematics: Combinatorics (Counting, Recurrence Relations, Generating Functions) · 2 marks · Numerical answer

S has ten elements. How many ordered tuples (A,B) of subsets of S satisfy A⊆B?

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Correct answer: 59049 to 59049

Explanation

For each element there are three allowed membership states: absent from both sets, present only in B, or present in both. Presence only in A is forbidden. Independent choices for ten elements give 3¹⁰=59049 ordered subset pairs.

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