Are any of the following implications always true? Prove or give a counter-example. a) f(n) = Θ(g(n)) ⇒  f(n) = cg(n) + o(g(n)), for some real constant c > 0. (Here small o) b) f(n) = Θ(g(n)) ⇒  f(n) = cg(n) + O(g(n)), for some real constant c > 0.(here big O) Please complete both

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A: Hello student Greetings Hope you are doing great. Thank you!!!

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