The set of all integral multiples of 5 is a subgroup of

Step-by-step solution

Let H consist of the integral multiple of 5 , i.e. H= 5 x: x I This H is the non-empty subset of I . Now, let a=5 r and b=5 ~s any two elements of H , where r and s are some integers. We have, a+b=5 r+5 s=5(r+8) 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.