Engineering Mathematics · Sets, Relations and Functions
Official IIT answer key · IIT Kharagpur · Audited Aug 2026
GATE CSE 2014 Set 3 Q49 · MCQ · 2 marks
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Topic notes
In this topic, GATE tests the foundational properties of finite sets, combinatorial counting of structured objects (such as matrices and function spaces), and the existence of mappings (injections, surjections, and bijections). The focus is on comparing cardinalities of constructed sets and understanding how equal or unequal cardinalities govern the existence of specific mapping types.
Full Sets, Relations and Functions guide →Consider the set of all functions f \0, 1, , 2014\ \0, 1, , 2014\ such that f(f(i)) = i, for all 0 i 2014. Consider the following statements: P. For each such function it must be the case that for every i, f(i) = i. Q. For each such function it must be the case that for some i, f(i) = i. R. Each such function must be onto. Which one of the following is CORRECT?
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