Exercise 1.6 (2)
2. Examine whether each of the following statement patterns is a tautology, a contradiction or a contingency
i) q ∨ [∼ (p ∧ q)]
Ans:
p | q | p ∧ q | ∼ (p ∧ q) | q ∨ [∼ (p ∧ q)] |
T | T | T | F | T |
T | F | F | T | T |
F | T | F | T | T |
F | F | F | T | T |
All the truth value in the last column are T. Hence , it is tautology.
ii) (∼ q ∧ p) ∧ (p ∧ ∼ p)
Ans:
p | q | ~p | ~q | ∼ q ∧ p | p ∧ ∼ p | (∼ q ∧ p) ∧ (p ∧ ∼ p) |
T | T | F | F | F | F | F |
T | F | F | T | T | F | F |
F | T | T | F | F | F | F |
F | F | T | T | F | F | F |
All the truth value in the last column are F. Hence , it is Contradiction.
iii) (p ∧ ∼ q) → (∼ p ∧ ∼ q)
Ans:
p | q | ∼ p | ∼ q | p ∧ ∼ q | ∼ p ∧ ∼ q | (p ∧ ∼ q) → (∼ p ∧ ∼ q) |
T | T | F | F | F | F | T |
T | F | F | T | T | F | F |
F | T | T | F | F | F | T |
F | F | T | T | F | T | T |
Truth Values in the last Column are not identical. Hence, it is Contingency.
iv) ∼ p → (p → ∼ q)
Ans:
p | q | ∼ p | ∼ q | p → ∼ q | ∼ p → (p → ∼ q) |
T | T | F | F | F | T |
T | F | F | T | T | T |
F | T | T | F | T | T |
F | F | T | T | T | T |
All the truth value in the last column are T. Hence , it is tautology.