By Newton's second law :
$$
\vec{F}_{e x t}=\frac{d p}{d t}
$$
As $\vec{F}_{e x t}$ in law of conservation of momentum is zero.
If $F_{e x t}=0, d p=0 \Rightarrow p=$ constant
Hence, momentum of a system will remain conserve if external force on the system is zero.
In case of collision between particle equal and opposite forces will act on individual particle by Newton's third law.
So, $\vec{F}_{12}=-\vec{F}_{21} \quad\left(\because \vec{F}_{e x t}=0\right)$
Total force on the system will be zero.
$$
\begin{aligned}
&\frac{d p_{12}}{d t}=-\frac{d \vec{p}_{21}}{d t} \text { or } d \vec{p}_{12}=-d \vec{p}_{21} \\
&\Rightarrow\left(d \vec{p}_{12}+d \vec{p}_{21}=0\right)
\end{aligned}
$$
So prove the law of conservation of momentum and verifies the option (d).