Exercise 1.6 (1)
1. Prepare truth tables for the following statement patterns.
i) p → (∼ p ∨ q)
Ans:
p | q | ~p | ~P ∨ q | p → (∼ p ∨ q) |
T | T | F | T | T |
T | F | F | F | F |
F | T | T | T | T |
F | F | T | T | T |
ii) (∼ p ∨ q) ∧ (∼ p ∨ ∼ q)
Ans:
p | q | ~ p | ~ q | ∼ p ∨ q | ∼ p ∨ ∼ q | (∼ p ∨ q) ∧ (∼ p ∨ ∼ q) |
T | T | F | F | T | F | F |
T | F | F | T | F | T | F |
F | T | T | F | T | T | T |
F | F | T | T | T | T | T |
iii) (p ∧ r) → (p ∨ ∼ q)
Ans:
p | q | r | ~q | p ∧ r | p ∨ ∼ q | (p ∧ r) → (p ∨ ∼ q) |
T | T | T | F | T | T | T |
T | T | F | F | F | T | T |
T | F | T | T | T | T | T |
T | F | F | T | F | T | T |
F | T | T | F | F | F | T |
F | T | F | F | F | F | T |
F | F | T | T | F | T | T |
F | F | F | T | F | T | T |
iv) (p ∧ q) ∨ ∼ r
Ans:
p | q | r | ~ r | p ∧ q | (p ∧ q) ∨ ∼ r |
T | T | T | F | T | T |
T | T | F | T | T | T |
T | F | T | F | F | F |
T | F | F | T | F | T |
F | T | T | F | F | F |
F | T | F | T | F | T |
F | F | T | F | F | F |
F | F | F | T | F | T |