$P$ vs $NP$ characterization confusion

Question

I know that $P \subseteq NP$, but for a problem in $P$, e.g. MST in a graph, is it a correct statement to say that:

The MST problem belongs in $NP-\text{Class}$.

(I mean, i think it is correct, but could someone classify that as wrong because he would expect $P$ instead of $NP$?)

Answer 1

$P$ is the class of problems which can be solved by a deterministic Turing machine in polynomial time and $NP$ is the class of problems which can be solved by a non-deterministic Turing machine in polynomial time. Since every deterministic turing maching can be simulated by a non-deterministic Turing machine then you have the corresponding inclusion. You may view the deterministic Turing machine as a branch in the tree of computations given by the non-deterministic Turing machine.