# Big-theta notation

I was wondering about big-theta ($\Theta$) notation.

A) Is $\Theta(n/2) \leq \Theta(n)$ for $n$ being an integer? I know that $n/2 = O(n)$, but does it also mean that $\Theta(n/2) \leq \Theta(n)$?

B) If I add two theta terms, so let's assume, we have: $\Theta(n) + 2*\Theta(n/2) + \Theta(n/3)$. Is that all $\Theta(n)$ or is it $\Theta(n) + \Theta(n/2) + \Theta(n/3)$. Again, for big-oh notation I just take the max when I add them, and I don't know if the same applies to big-theta.

Since $n = O(n/2)$ is also true, as $n \le 2 (n/2)$, you get $\Theta(n)= \Theta(n/2)$.
For B, yes this is all just $\Theta(n)$. Recall the first part and note $\Theta(n)+\Theta(n) = \Theta(n)$.