If g(n) is a upper bound of f(n), then g(n) is not a lower bound on f(n).

I think this statement above is false because if f(n) ∈ theta(1), which means the running time of f(n) is constant (ex. f(n) = 1), then this is a counter example of the above statement.

If c_{1}(g(n)) <= f(n) <= c_{2}(g(n))

then let g(n), c_{1}, c_{2}= 1.

1<=1<=1

which is true for all n >= x_{0}for some x_{0}> 0.

Is this correct?