# Finding the smallest equivalence relation containing a specific list of ordered pairs

I'm having trouble trying to understand the smallest equivalence relation containing a specific subset.

Q: Find the smallest equivalence relation $R$ on $M = \{1,2,3,4,5\}$ which contains the subset $R_0 = \{(1,1), (1,2), (2,4), (3,5)\}$

I know this is probably really simple but I just cant get it. Is anyone able to explain this to me? I've tried to find explanations elsewhere, but nothing I can find talks about the smallest equivalence relation.

• First, is $R_0$ an equivalence relation? If not, can you think of elements that you could add to $R_0$ to make it an equivalence relation? Once you can do that, you can then start to think about how to do this minimally". – Matthew Conroy Aug 31 '16 at 0:54