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Please explain the answers and how you got them. I know that a is False and you have to give a counter example, but how is it found? What is an example?

2) (4 pts) Let fi and f2 be asymptotically positive non-decreasing functions. Prove or disprove each of the following conjectures. To disprove give a counter example. If f,(n) : Ω(g(n)) and fan) ()(g(n)) thcnJi(n), Θ (f)(n) ) a. b. If fi(n) - O(g/ /(n)) and j2( n) - O(g^n)) then fi(n)+ f(n)- O(g(n) +g(n))

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