Consider the following two statements:

            A) Linear momentum of a system of particles is zero

            B) Kinetic energy of a system of particles is zero

Here we are given two statements and asked to evaluate their implication.

            (i) Statement (A) refers that the linear momentum of system of particles is zero.This implies that the K.E of system of particles is not zero because linear momentum of each particle can be negative or positive but their K.E is always positive.

            (ii) Statement (B) refers that K.E of system of particles is zero means the K.E of ever particle

            is zero this implies that linear momentum of system of particles must be zero.

            So we can conclude that A does not imply B but B implies A.