Given the following statements :
$S_{1}$ : The subgraph-isomorphism problem takes two graphs $G_{1}$ and $G_{2}$ and asks whether $G_{1}$ is a subgraph of $G_{2}$ .
$S_{2}$ : The set-partition problem takes as input a set $S$ of numbers and asks whether the numbers can be partitioned into two sets $A$ and $\bar{A}=S-A$ such that
$\begin{matrix} \sum x & & \sum x \\ & = & \\ x \in A & & x \in \bar{A} \end{matrix}$
Which of the following is true ?
- $S_{1}$ is $NP$ problem and $S_{2}$ is $P$ problem.
- $S_{1}$ is $NP$ problem and $S_{2}$ is $NP$ problem.
- $S_{1}$ is $P$ problem and $S_{2}$ is $P$ problem.
- $S_{1}$ is $P$ problem and $S_{2}$ is $NP$ problem.