 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability/3/e/i/solution

Since

h (n) = max {f (n), g (n)}

, both

f (n) \leq h (n)

and

g (n) \leq h (n)

. Therefore

f (n) + g (n) \leq 2 h (n)

for every positive

n

. The definition of big O notation is satisfied with constant

2

and threshold

1

. True: $f + g = O (h)$ .

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