Gate CS-2014-3 Question Paper With Solutions

Q. 59 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: (B)

Explanation:

Gate CS-2014-3 Question Paper With Solutions

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