Answer
$p|(q|r)$ and $(p|q)|r$ are not logically equivalent.
Work Step by Step
Two propositions are logically equivalent if they have the same truth value for any combination of truth values of the variables.
p NAND q is true if and only if both p or q or both are false.
p NAND q is denoted as p|q
$\underline{p\quad q \quad r\quad q|r\quad p|q\quad p|(q|r)\quad (p|q)|r}$
$T\quad T \quad T\quad F\quad F\quad\quad T\quad\quad\quad T$
$T\quad T \quad F\quad T\quad F\quad\quad F\quad\quad\quad T$
$T\quad F \quad T\quad T\quad T\quad\quad F\quad\quad\quad F$
$T\quad F \quad F\quad T\quad T\quad\quad F\quad\quad\quad T$
$F\quad T \quad T\quad F\quad T\quad\quad T\quad\quad\quad F$
$F\quad T \quad F\quad T\quad T\quad\quad T\quad\quad\quad T$
$F\quad F \quad T\quad T\quad T\quad\quad T\quad\quad\quad F$
$F\quad F \quad F\quad T\quad T\quad\quad T\quad\quad\quad T$
Since the last two columns of the truth table $\underline{do not}$ contain the same truth value in every row, the last two expressions are NOT logically equivalent.
Hence the logical operator | is not associative.
