Correct Answer.
To see that (p 
q ) 
(r
q) has a truth table as claimed in column 3, let us ask
under which circumstances this formula can evaluate to F. Since the
formula is a disjunction, this can only happen if
both disjuncts (p q ) and (r
q) evaluate to F. For the former,
which is an implication, this can only happen if its
premise p is true and its conclusion q is false. For the latter, which
is a negation, this can only happen if (r q)
evaluates to T. But since this is a conjunction, that
forces r to be T. Note that this valuation actually makes the entire
formula false and that this corresponds to row 3 in column 3, the
only F entry of that column.
Back to Question.
Next Question.