The cardinality of the power set of { 0, 1, 2, , 10 } is …
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GATE CSE 2015 Set 2 · Q18
NAT1 markEasy
Time
The cardinality of the power set of is _______.
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Solution
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Official answer: 2048
Sets, Relations and FunctionsLet .
The number of elements in the set is:
The power set of , denoted as , is the set of all subsets of . The cardinality of the power set of any finite set with elements is given by .
Therefore, the cardinality is:
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Examiner trap
The misconception this question tests
Count the number of elements in the given set (including 0), and then compute .
This Sets, Relations and Functions previous year question is Q18 of the GATE CSE 2015 Set 2 paper. Find more GATE CSE PYQs on Sets, Relations and Functions in Engineering Mathematics, or browse all GATE CSE PYQs.
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Sets, Relations and Functions in GATE CSE
Sets, Relations and Functions has 5 GATE CSE PYQs across 5 papers from 2014 to 2024. 2 of them are 1-mark NAT questions like this one, and it is the only one in GATE CSE 2015 Set 2.
How GATE tests Sets, Relations and FunctionsMore from GATE CSE 2015 Set 2
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- Q15Consider the following function written in the C programming language. void foo(char *a){ if ( *a && *a != ' '){ foo(a+1); putchar(*a); } } The output of the a…MCQ1 markEasy
Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.