Finding the symmetric and reflexive closure of the relation $R = \{(a, b) | a > b\}$ on the set of positive integers.
For symmetric closure I have: $R = \{(a, b) | a > b\} U \{(b, a) | a > b\} = \{(a, b) | a \neq b\}$.
To make it reflexive and symmetric I tried: $\{(a, b) | a \neq b\} U \{(a,a) | a \in Z^+ \}$
But I don't know how to proceed from there because then I'd have the first set saying that $a \neq b$ and the second saying a is equal to itself.