Friendly Set (self-made)

[Fm Jakaria]

Let X be a nonempty set of rational numbers; so that for any two elements a and b of X, a-b also belongs to X.
A finite nonempty set F of rational numbers is said to be a 'friend' of X; if for any element c of X, there exists elements a(1),a(2),.....,a(i) of F and integers r(1), r(2),......, r(i) such that
c = a(1)r(1)+a(2)r(2)+......+a(i)r(i); where i is greater than 1 and each r(j) is either 1 or -1.

Prove that if X has at least one friend; then the friend of X that has lowest cardinality must have cardinality 1.