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1. Prove that (f(n))(g(n))=(f(n)g(n)). [Hint: Prove that h(n)(f(n))(g(n))h(n)(f(n)g(n)), and h(n)(f(n))(g(n))h(n)=(n)(n),forsome(n)(f(n)),(n)(g(n).] I. Prove that e (f e (9(n)) g(n)). [Hint: Prove that h(n) h(n) g(n)), and
1. Prove that (f(n))(g(n))=(f(n)g(n)). [Hint: Prove that h(n)(f(n))(g(n))h(n)(f(n)g(n)), and h(n)(f(n))(g(n))h(n)=(n)(n),forsome(n)(f(n)),(n)(g(n).]
I. Prove that e (f e (9(n)) g(n)). [Hint: Prove that h(n) h(n) g(n)), and h(n) h(n) = o(n) for some o(n) e (n) I
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