1. If f=O(g), then g=O(f) 2. If f=O(g) and g=O(h), then f=O(h) 3. if f=O(g) and g=O(f) and ?n, f(n)g(n) then f-g=O(1) 4. If f=O(g) and g=O(f), then f/g=O(1) 5. If f=O(g) and h=O(g), then f=O(h) f = O(g) is defined for functions f and g (both from N to N) to mean that there exist positive constants no and C such th

Question

f = O(g) is defined for functions f and g (both from N to N) to mean that there exist positive constants
no and C such that:

1. If f=O(g), then g=O(f)

2. If f=O(g) and g=O(h), then f=O(h)

3. if f=O(g) and g=O(f) and ?n, f(n)>g(n) then f-g=O(1)

4. If f=O(g) and g=O(f), then f/g=O(1)

5. If f=O(g) and h=O(g), then f=O(h)

f = O(g) is defined for functions f and g (both from N to N) to mean that there exist positive constants no and C such that: f(n) ? C· g(n) for all n ? no. For each of the following statements either prove the statement if it is true or otherwise provide a counter- example and justify why your counterexample is indeed a counter-example:

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Expert Answer to -      1. If f=O(g), then g=O(f) 2. If f=O(g) and g=O(h), then f=O(h) 3. if f=O(g) and g=O(f

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Solution for -      1. If f=O(g), then g=O(f) 2. If f=O(g) and g=O(h), then f=O(h) 3. if f=O(g) and g=O(f

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This an additional answer to -      1. If f=O(g), then g=O(f) 2. If f=O(g) and g=O(h), then f=O(h) 3. if f=O(g) and g=O(f

(Solved): 1. If f=O(g), then g=O(f) 2. If f=O(g) and g=O(h), then f=O(h) 3. if f=O(g) and g=O(f ...

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