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Let f1 and f2 be asymptotically positive non-decreasing functions. Prove or disprove each of the following conjectures. To disprove give a counter example. a. If

Let f1 and f2 be asymptotically positive non-decreasing functions. Prove or disprove each of the following conjectures. To disprove give a counter example.

a. If f1(n) = O(g(n)) and f2(n) = O(g(n)) then f1(n)+ f2(n) = O(g(n)).

b. If f(n) = O(g1(n)) and f(n) = O(g2(n)) then g1(n) = (g2(n) )

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