Correct Answer.
Let us consider all the possibilities in a truth table,
| p |
q |
|
|
p  q |
p  q |
(p q)  (p q) |
| T |
T |
|
|
T |
F |
T |
| T |
F |
|
|
F |
T |
T |
| F |
T |
|
|
F |
T |
T |
| F |
F |
|
|
T |
F |
T |
We find that the formula is always true.
We can also reason this in the manner done previously. The formula
(p q) (p q) is a disjunction, so it can only evaluate to F of its
two disjuncts p q and
p q
evaluate to F. But the first disjunct can only compute F iff p and q get
assigned different truth values, and this forces the second disjunct to be
T. Thus, it is not possible for the formula to evaluate to F.
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