I'm attempting to prove the transitive relation on $\theta$ and I'm having trouble understanding the meaning of one of the symbols used. Here is the transitive relation:
$f(n) = \theta(g(n)) \bigwedge g(n) = \theta(h(n)) \longrightarrow f(n) = \theta(h(n))$
What does the "and" means with respect to $\theta(g(n)) \bigwedge g(n)$?
I think the correct interpretation is:
$f(n) = \Theta(g(n)) \quad \land \quad \left(g(n) = \Theta(h(n))\right) \quad \implies \quad f(n) = \Theta(h(n))$
It means that $f(n)$ is roughly a multiple of $h(n)$.
see this link to understand the Theta function ($\Theta$).