I have question about set theory again. I have non-empty set $A$, and set $K$ of all equivalence relations on $A$. $K$ is partially ordered set regarding subsets ($\subseteq$). now I need to find the greatest element and the least element in $K$. so I think that the greatest element is the relation $A \times A$ and the least element is $\varnothing$, am I wrong?.
Now, they say that $A = \{1,2,3,4\}$. and they move the greatest element and least element to new set named $L$. the set $L$ is also partially ordered set regarding subsets ($\subseteq$). and I need to find two different maximal elements and two different minimal elements.
So if I understand correctly the question, the set $L$ should be $\{\varnothing, A \times A\}$. but how I can find two different elements in this set if the set consists of two elements?
I think there is something here that I don't understand. I will be glad if someone will tell me how to continue from here.
Thanks in advance.