Let $Q = \{A,B,C\}$.
I argue that a relation on A that is symmetric and Anti-symmetric but neither reflexive nor transitive is the relation $R$ such that $R =\{\}$. This I think is correct because both symmetry and anti-symmetry are "if...then" statements and if the "if" is false, then it is vacuously true meaning that $\{\}$ is symmetric and anti-symmetric
I also have another answer that goes as $R = \{(A,A), (B,B)\}$. This second answer is because I interpreted neither.. nor as not ($A$ or $B$) which is not $A$ and not $B$. So, I only had to make sure it is not reflexive to make the second part false (since symmetry and anti-symmetry imply transitivity)
Which of my answers are correct please. If none, can anyone give a correct answer