Find subrings of $\mathbb Z_{18}$ which illustrate the following:
A is a ring with unity, B is a subring of A, but B is not a ring with unity.
A and B are rings with unity, B is a subring of A, but the unity of B is not the same as the unity of A.
So for both 1 and 2, I would let A=$\mathbb Z_{18}$. The unity is 1. for 1. B={0,3,6,9,12,15}. This is a subring since its closed under addition and multiplication but it does not have the unity=1. However when I look at 2. I would say maybe B= {0,9} but then I get that B doe not have the unity=1, making me think that 0 is the unity for B.