Consider f(n) and g(n) be asymptotic non-negative functions.

So here can we say that min(f(n), g(n)) = Θ(f(n) + g(n))

My proof for this

For f(n) = Θ(g(n))

c1*g(n) $\leq $ f(n) $\leq $ c2*g(n) such that c1, c2 >0

Considering the above definition suppose, f(n) = $n^{2}$ and g(n) = $n^{3}$

min($n^{2}$, $n^{3}$) = $n^{2}$

Now for this we can write like 0.001*($n^{3}$ + $n^{2}$) $\leq $ $n^{2}$ $\leq $ 1* ($n^{3}$ + $n^{2}$)

So thus we can say that min(f(n), g(n)) = Θ(f(n) + g(n))

Is this the correct way? What would be the correct answer?