Let $x$ and $y$ be strings and let $L$ be any language. We say that $x$ and $y$ are $\text{distinguishable}$ by $L$ if some string $z$ exists whereby exactly one of the strings $xz$ and $yz$ is a member of $L;$ otherwise, for every string $z,$ we have $xz\in L$ whenever $yz\in L$ and we say that $x$ and $y$ are $\text{indistinguishable}$ by $L.$ If $x$ and $y$ are indistinguishable by $L,$ we write $x ≡L y$. Show that $≡L$ is an equivalence relation.

A $\text{palindrome}$ is a string that reads the same forward and backward.