I was studying Theory of Computation and I'm kind of lost in solving this problem.
Let $R$ be a relation defined on the set of states $Q$ of a DFA as $q_1Rq_2$ if $\delta(q_1,a)=\delta(q_2,a)$ for some $a\in\Sigma$.
Is $R$ an equivalence relation? Prove.
So to prove that $R$ is an equivalence relation, I have to show that
- $R$ is reflexive
- $R$ is symmetric
- $R$ is transitive
But since it's related to DFA, I'm not sure how to approach this problem. Some help is much appreciated.