Question: I need help with problem 3, specifically counter examples to a-c Show the following using the definitions of 0, 2, and O. (1) (2 points)

I need help with problem 3, specifically counter examples to a-c

Show the following using the definitions of 0, 2, and O. (1) (2 points) 2n + n +4 On") (2) (2 points) 3n" - 9n + 4n (n) (Hint: careful with the negative number) (3) (4 points) Suppose f(n) (91(n)) and f(n) (92(n)). Which of the following are true? Justify your answers using the definition of O. Give a counter example if it is false. (a) f(n) 0(5.91(n) + 100 ) (b) f(n) E O gi(n) +g2(n)) (c) f(n) E O 9.n) (d) f(n) O( max(91(n), 92(n)))

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