For each problem, make sure to rewrite the asymptotic notation to whatever the expression is defined to be mathematical, by spelling out the definition. Also keep in mind that you need to provide, whenever applicable, concrete constants and n₀ when proving an assertion or a counterexample when disproving an assertion.

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3.1-1 Let f(n) and g(n) be asymptotically nonnegative functions. Using the basic definition of -notation, prove that max(f(n),g(n))=(f(n)+g(n)). 3.12 Show that for any real constants a and b, where b>0, (n+a)b=(nb)