Centre of Mass and Collision Part 1

In completely inelastic collision,
m1v1+m2v2=m1v+m2v
after collision both particle have common velocity v, so all energy is not lost
∴ Statement −1 is true
The principle of conservation of momentum applicable for all kinds of collisions.
So statement −2 is also true.
Statement - 2 explains statement - 1 correctly because applying the principle of conservation of momentum, we can get the common velocity and hence the kinetic energy of the combined body.