Set Theory and Algebra GATE 2014 Question #10009 with Solution

GATE 2014 · session-3

Engineering MathematicsSet Theory and AlgebramediumMCQ2 marks

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?

AP, Q and R are trueBOnly Q and R are trueCOnly P and Q are trueDOnly R is true

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