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For each of the statements below, state whether it is true or false and then prove your answer.

(a) 15n 3 log n + 10n 2 + 50 is O(n 3 log n).

(b) 3n 2 − 12n + 2 is Ω(n 3 )

(c) 2n+1 is Θ(2n )

(d) 22n is O(2n )

(e) log(n!) is O(n log n) (Hint: compare n! and n n )

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For each of the statements below, state whether it is true or false and then prove your answer.
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