q )
(r
q) does not have the truth table as claimed in column 5, we
can check that its first row matches the semantics of that
formula. However, in row 2 the atoms p and q are true, whereas r is
false. This makes the implication (p
q) true. Therefore, the entire
formula, which is a disjunction, evaluates to T,
since one of its disjuncts, namely (p
q ), does so. This contradicts the entry in row 2 of
column 5.