Question

Let (i) (P ∨ q) ∨ (p ∨ ~ q), (ii) (P ∧ q) ∧ (p ∨ ~ q), (iii) (P ∨ q) ∧ (p ∨ ~ q), (iv) (P ∨ q) ∨ (p ∧ ~ q), which one is tautology

(1) (i)

(2) (ii)

(3) (iii)

(4) (iv)

Answer 1

Correct option (1) (i)

Explanation:

(i) (P ∨ q) ∨ (p ∨ ~ q) = p ∨ (q ∨ ~ q) = P ∨ t = t

(ii) (P ∨ q) ∧ (p ~ q)

(iii) (P ∨ q) ∧ (p ∨ ~ q) = p ∨ (q ∨ ~ q) = P ∨ f = p

(iv) (P ∨ q) ∨ (p ∧ ~ q)

| p | q | ~ q | P ∨ q | p ∨ ~ q | (P ∨ q) ∧ (p ∨ ~**q)**, |
| T | T | F | T | F | T |
| T | F | T | T | T | T |
| F | T | F | T | F | T |
| F | F | T | F | F | F |

(P ∧ q) ∧ (p ∨ ~ q)

| p | q | ~ q | P ∧ q | p ∧ ~ q | (P ∨ q) ∧ (p ∨ ~**q)**, |
| T | T | F | T | T | T |
| T | F | T | F | T | F |
| F | T | F | F | F | F |
| F | F | T | F | F | F |