GATE CSE 2021 Set 2 Q60: Number of pairs (A, B) of subsets with A ⊆ B ⊆ S, |S| = 10

Engineering Mathematics
2 marks
NAT
No negative marking

Let $S$ be a set consisting of 10 elements. The number of tuples of the form $(A, B)$ such that $A$ and $B$ are subsets of $S$ , and $A \subseteq B$ is ________.

Try it: numerical answer: type the value

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Numerical answer. No negative marking.

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Answer: 59049 (official GATE 2021 final answer key)

Concept used: Count element by element: each element independently picks one of the allowed memberships.

First step: Each element of $S$ is in neither set, in $B$ only, or in both $A$ and $B$ : 3 choices each.

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Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

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GATE CSE 2021 Set 2 Q60: Number of pairs (A, B) of subsets with A ⊆ B ⊆ S, |S| = 10

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