Answer
See step by step work for solution.
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 p|q \quad q|p} $
$ T\quad T \quad F \quad F $
$ T\quad F \quad T \quad T $
$ F\quad T \quad T \quad T $
$ F\quad F \quad T \quad T $
Since the last two columns of the truth table contain the same truth value in every row, the last two expressions are logically equivalent.
