Answer
$p$ and $q$ are equivalent means that the the truth table of $p$ and $q$ are same. Now if we say that $p$ and $q$ are equivalent and $q$ and $r$ are equivalent, it means that the truth table of $p$ and $q$ is same and the truth table of $q$ and $r$ is also same. It implies that the truth table of $p$ and $r$ are also same which means $p$ and $r$ are also logically equivalent.
Work Step by Step
Same as above.
