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

p	q	~p	~q	~p∨~q	p∧q	~p∨~q	(~p∨~q↔~(p ∧ q)
T	T	F	F	F	T	F	T
T	F	F	T	T	F	T	T
F	T	T	F	T	F	T	T
F	F	T	T	T	F	T	T

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