Prove why f(n)=big omega(g(n)) then f(n)=o(g(n)) is NEVER TRUE. Prove why f(n) +g(n) =Theta(max(f(n),g(n)) is ALWAYS...

Prove why f(n)=big omega(g(n)) then f(n)=o(g(n)) is NEVER TRUE.

Prove why f(n) +g(n) =Theta(max(f(n),g(n)) is ALWAYS TRUE

Solutions

Expert Solution

Here we will use the basic definitions of omega asymptotic function, small-o asymptotic function and theta asymptotic function while solving these problems.

1) First of all, we will consider f(n)=big omega(g(n)) :

We have proved that f(n)=big omega(g(n)) then f(n)=o(g(n)) is never true.

2) We have to note that the result of max(f(n),g(n)) is either f(n) or g(n) [ i.e. whichever is maximum will be the result]

The sum of f(n) and g(n) is always greater than or equal to individual f(n) and individual g(n).

We have proved that f(n) +g(n) =Theta(max(f(n),g(n)) is always true.

venereology answered 1 year ago

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