Let H consist of the integral multiple of 5, i.e. H={5x:x∊I} This H is the non - empty subset of I. Now, let a=5r and b=5s any two elements of H, where r and s are some integers. We have, a+b=5r+5s=5(r+s)∊H. (r+s) comes out to be the some integer. ∴a∊H,b∊H⇒(a+b)∊H Hence H is a subgroup of set of all integers under addition.