Let A n sinv Z 5r for some integer r and B m sinv Z m 20

Let A = {n sinv Z\ = 5r for some integer r} and B = {m sinv Z\\ m = 20s for some integer s} Is A SubsetEqual B? Explain. Is B SubsetEqual A? Explain.

Solution

Given:  
   A = {n element of Z / n = 5r for some r}
   B = {m element of Z / m = 20s for some r}

   So, B = {set of Z that are multiple of 20}
   and A = {set of Z that are multiple of 5}

   Since 20 is multiple of 5 (5*4), hence all the
   elements of B are multiple of 5

   Hence, A is subset of B

   a) true
   b) false