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3. Suppose T(n) = O(f(n)) and R(n) = O(g(n)) for positive valued functions T(n), R(n), f(n), g(n), for n>=1. 1. Prove that: T(n) + R(n)

3. Suppose T(n) = O(f(n)) and R(n) = O(g(n)) for positive valued functions T(n), R(n), f(n), g(n), for n>=1.

1. Prove that: T(n) + R(n) = O( f(n) + g(n) )

2. Prove that T(n)R(n) = O( f(n)g(n) )

3. Disprove the claim that T(n)/R(n) = O( f(n)/g(n) ), i.e., provide a counter example.

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3. Suppose T(n) = O(f(n)) and R(n) = O(g(n)) for positive valued functions T(n), R(n), f(n), g(n), for n>=1. 1. Prove that: T(n) + R(n)

3. Suppose T(n) = O(f(n)) and R(n) = O(g(n)) for positive valued functions T(n), R(n), f(n), g(n), for n>=1. 1. Prove that: T(n) + R(n) = O( f(n) + g(n) ) 2. Prove that T(n)*R(n) = O( f(n)*g(n) ) 3. Disprove the claim that T(n)/R(n) = O( f(n)/g(n) ), i.e., provide a counter example.

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3. Suppose T(n) = O(f(n)) and R(n) = O(g(n)) for positive valued functions T(n), R(n), f(n), g(n), for n>=1.

1. Prove that: T(n) + R(n) = O( f(n) + g(n) )

2. Prove that T(n)R(n) = O( f(n)g(n) )

3. Disprove the claim that T(n)/R(n) = O( f(n)/g(n) ), i.e., provide a counter example.