binary relation that is both symmetric and irreflexive I was asked to find a binary relation on $A$ that is symmetrical and irreflexive, and which is also a function from $A$ to $A$ where $A=\{1,2,3,4\}$
so i don't know if its correct but i came up with these $\{<1,2>, <1,3>, <1,4>, <2,1>, <2,3>, <2,4>, <3,1>, <3,2>, <3,4>, <4,1>, <4,2>, <4,3>\}$

This relation appears to be symmetric and irreflexive, but it's not a function, because the same domain values appear multiple times with different range values, i.e., it does not pass the "vertical line test".
For a relation to be a function on a $4$-element set, it needs to have exactly $4$ ordered pairs in it, one to map each value somewhere.
