(i) (p ∧~q) → (p∧q)
| p |
q |
~q |
(a) p ∧~q |
(b) p∧q |
(a) → (b) |
| T |
T |
F |
F |
T |
T |
| T |
F |
T |
T |
F |
F |
| F |
T |
F |
F |
F |
T |
| F |
F |
T |
F |
F |
T |
It is neither Tautology nor contradiction
(ii) [~p ∧ (p ∨ q)] → q
| p |
q |
p ∨ q |
~p |
~p ∧ (p ∨ q) |
[~p ∧ (p ∨ q)] → q |
| T |
T |
T |
F |
F |
T |
| T |
F |
T |
F |
F |
T |
| F |
T |
T |
T |
T |
T |
| F |
F |
F |
T |
F |
T |
F From last column we conclude it is a tautology
(iii) (p →q) ↔ (~p →~q)
| p |
q |
a p →q |
~p |
~q |
~p →~q |
a → b |
| T |
T |
T |
F |
F |
T |
T |
| T |
F |
F |
F |
T |
T |
T |
| F |
T |
T |
T |
F |
F |
F |
| F |
F |
T |
T |
T |
T |
T |
F It is neither a tautology nor contradiction
(iv) [~(p →~q)] ∨ (~ p ↔ q)
| p |
q |
~q |
p →~q |
~(p →~q) a |
~ p |
~ p ↔ q b |
a∨b |
| T |
T |
F |
F |
T |
F |
F |
T |
| T |
F |
T |
T |
F |
F |
T |
T |
| F |
T |
F |
T |
F |
T |
T |
T |
| F |
F |
T |
T |
F |
T |
F |
F |
It is neither tautology nor contradiction
(v) (~p ∨ q) ↔ (p ∨~q)
| p |
q |
~q |
~p ∨ q a |
~q |
p ∨~q b |
a↔b |
| T |
T |
F |
T |
F |
T |
T |
| T |
F |
F |
F |
T |
T |
F |
| F |
T |
T |
T |
F |
F |
F |
| F |
F |
T |
T |
T |
T |
T |
It is neither tautology nor contradiction
