Official PYQ · 2015Set 2 · Q18Sets, Relations and FunctionsNAT1 mark

GATE CS 2015 Set 2 Q18 — Sets, Relations and Functions

The cardinality of the power set of

\{0, 1, 2, \dots , 10\}

is _______

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Answer: 2048

Let the given set be $S = \{0, 1, 2, \dots, 10\}$ .

First, we determine the cardinality (the number of elements) of the set $S$ :

The elements are integers starting from $0$ up to $10$ .
The number of elements, $|S| = 10 - 0 + 1 = 11$ .

The power set of $S$ , denoted by $\mathcal{P}(S)$ , is the set of all subsets of $S$ . If a set has $n$ elements, the cardinality of its power set is given by the formula:

$\lvert\mathcal{P}(S)\rvert = 2^n$

Substituting $n = 11$ into the formula:

$\lvert\mathcal{P}(S)\rvert = 2^{11} = 2048$

Thus, the cardinality of the power set is 2048.

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Published 10 Oct 2026

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