n many programming languages, there are two distinct but related notions of “equality”: has the same value as and is the same object as. In Python, these are denoted as == and is, respectively; in...

n many programming languages, there are two distinct but related notions of “equality”: has the same value as and is the same object as. In Python, these are denoted as == and is, respectively; in Java, they are .equals() and ==, respectively. (Confusingly!) (For example, in Python, 1776 + 1 is 1777 is false, but 1776 + 1 == 1777 is true.) Does one of these equality relations refine the other? Explain.

1. List all partial orders on {0, 1}.

2. List all partial orders on {0, 1, 2}