Prove that the following statement pattern is a tautology. (~ p ∨ ~ q) ↔ ~ (p ∧ q)

EXERCISE 1.6Q 3.4   PAGE 16
Exercise 1.6 | Q 3.4 | Page 16

Prove that the following statement pattern is a tautology.

(~ p ∨ ~ q) ↔ ~ (p ∧ q)


SOLUTION

pq~p~q~p∨~qp∧q~p∨~q(~p∨~q↔~(p ∧ q)
TTFFFTFT
TFFTTFTT
FTTFTFTT
FFTTTFTT

All the truth values in the last column are T. Hence, it is a tautology.