GATE | GATE-CS-2014-(Set-3) | Question 62

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?

(A)

P, Q and R are true

(B)

Only Q and R are true

(C)

Only P and Q are true

(D)

Only R is true

Answer

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