The question is:
Let $A = \{\text{cat, dog, mouse, bird}\}$ and let $R$ be the binary relation on $A$ given by $R = \{(x,y) \mid \text{$x$ and $y$ have no letter in common}\}$.
(a) Draw $R$.
(b) State whether or not $R$ is an equivalence relation, explaining your answer.
I have done both parts of the question, and wanted to confirm if the answers and my reasoning behind the answers are correct, and would be acceptable for an exam answer.
(a)
(b)
No, it is not an equivalence relation, as the relation is not reflexive. An example contradiction would be $R(\text{dog, dog})$, which is not reflexive, because they have letters in common.