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Algorithms Homework 4

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Homework 4

Use the formal definitions of Big-Oh, Big-Omega, and Big-Theta to prove
the following.
1. Prove that f(n) = Θ(g(n)) if and only if f(n) = O(g(n)) and f(n) =
Ω(g(n)).
2. Prove that if f1(n) = Ω(g1(n)) and f2(n) = Ω(g2(n)), then f1(n)+f2(n) =
Ω(g1(n) + g2(n)).
1

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